42 E This histogram shows battery life (in hours) of 40 batteries of the same brand. When reading a histogram, it is important to look at the shape, center and spread of the data. Relative Frequency 0.30 100 110 120 130 Battery Life (hours) 140 150 Complete the following statements about the shape of the data shown.
A. The distribution of the data is approximately
B. The mean battery life is
Answers
The answer of the given question based on the histogram that shows battery life is, (A). The distribution of the data is approximately symmetric. (B). The mean battery life is around 125 hours.
What is Data distribution?Data distribution refers to pattern or shape of how data is spread out or distributed over range of values. It is important to understand distribution of data because it can provide insights into nature of the data and inform statistical analysis.
There are several ways to describe distribution of data, including measures of center (like mean, median, and mode) and measures of spread (like range, variance, and standard deviation)
A. The distribution of the data is approximately symmetric.
B. The mean battery life can be estimated by finding the center of the histogram, which appears to be around 125 hours. However, without knowing the exact bin widths or the midpoint of each bin, it is difficult to estimate the mean precisely.
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Based on the histogram that displays energy life, the following is the response to the question:
a). The data are distributed in a roughly symmetrical manner.
b). An average charge lasts for about 125 hours.
What is Data distribution?Data distribution describes the way that data is dispersed or distributed across a variety of values. Understanding data distribution is crucial because it can shed light on the character of the data and help with statistical analysis.
Measures of the center (like mean, median, and mode) and measures of spread are two methods to describe data distribution. (like range, variance, and standard deviation).
A). The facts are distributed in a roughly symmetrical manner.
B). You can determine the average battery life by locating the histogram's center, which looks to be 125 hours.
It is challenging to calculate the mean exactly without knowing the precise bin widths or the midpoint of each bin, though.
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The image of the question attached below,
Related Questions
A discounted amusement park ticket costs $44 dollars, which is $12.95 less
than the original price p. Write and solve an equation to find the original
price.
Answers
Answer:
p-(p*.2274)
Step-by-step explanation:
P is the original price
P multiplied by .2274 gives the discount that's taken off
So the answer is P minus the discounted sum
3 workers can do a job in 28 hours, how many more workers are needed to complete the job in 12 hours
Answers
Answer:
7 workers are required, so we need 7-3 or 4 more workers.
Step-by-step explanation:
Can you please help me with this problem
Answers
Answer:
X = 35°
Y = 72.5°
Step-by-step explanation:
x is vertically opposite to 35° so x = 35°
35 × 2 = 70
360 - 70 = 290
290 / 4 = 72.5
Y = 72.5°
Answer:
x = 35
y = 72.5
Step-by-step explanation:
At your level, it is assumed that those lines are straight. Keeping this in mind, we can find the answer to this problem.
First, we have to find x.
x = 35º because opposite angles are equal (xº is opposite to 35º).
Then, we have to calculate y.
You should know that angles in a straight line add up to 180º.
So: yº + yº + 35º = 180º
You know have to solve this equation (solve for y).
y + y + 35 = 180
y + y = 180 - 35
y + y = 145
2y = 145
y = 145 / 2
y = 72.5
Check: 72.5 + 72.5 + 35 = 180
Given the graph of y = a sin b(x + c) +d, determine the amplitude.
A -1
C 6
B
3
D 12
- 27
9 Y
2T
Answers
Answer:
Step-by-step explanation:
The general equation for a sinusoidal function of the form y = a sin b(x + c) + d is:
a is the amplitude (the maximum displacement from the midline).
b determines the period (the distance between two consecutive peaks or troughs).
c is the horizontal shift (the amount by which the graph is shifted horizontally).
d is the vertical shift (the amount by which the graph is shifted vertically).
From the given information, we can see that:
The amplitude is not given.
b = 3, which means the period is 2π/3.
c = 6, which means the graph is shifted 6 units to the left.
d = 9, which means the graph is shifted 9 units up.
Since the amplitude is not given, we need to look at the graph to determine it. However, the graph is not provided, so we cannot determine the amplitude with the given information.
Find the interest rate for the given deposit and compound amount.
$4000 accumulating to $5994.75, compounded monthly for 7 years.
Answers
Answer:
The interest rate is 5.79% (to the nearest hundredth).
Step-by-step explanation:
To find the interest rate for the given deposit of $4000 accumulating to $5994.75, compounded monthly for 7 years, use the compound interest formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $4,000A = $5,994.75n = 12 (monthly)t = 7 yearsSubstitute the given values into the formula and solve for r.
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{12 \times 7}[/tex]
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \dfrac{5994.75}{4000}=\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}=1+\dfrac{r}{12}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1=\dfrac{r}{12}[/tex]
[tex]\implies \sf r=12\left(\sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1\right)[/tex]
[tex]\implies \sf r=0.057937950...[/tex]
[tex]\implies \sf r=5.7937950...\%[/tex]
Therefore, the interest rate is 5.79% (to the nearest hundredth).
What is the slope of the line containing (–2, 5) and (4, –4)? A. -2 B. 1 C. 1/2 D. -1/2
Answers
The slope of the line on this graph with points (2, 5) and (4, 4) is equal to: D. =1/2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (5 - 4)/(2 - 4)
Slope (m) = -1/2
In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to -0.5 or -1/2.
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In a large population of nurses, suppose 20% of the nurses would prefer the night shift. If a random sample of 10 nurses is taken, what is the probability less than 3 are nurses that prefer the night shift?
Answers
We can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of nurses in the sample who prefer the night shift.
Using the binomial probability formula, we can calculate:
P(X = 0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(X = 1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(X = 2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3019
Therefore,
P(X < 3) = 0.1074 + 0.2684 + 0.3019 = 0.6777
The probability that less than 3 nurses in the sample prefer the night shift is approximately 0.6777 or 67.77%.
Which statement is true?
Answers
The correct statement about diagram is m∠1 > m∠4. So correct option is D.
Describe Angles?In mathematics, an angle is a measure of the amount of rotation between two rays or line segments that share a common endpoint, known as the vertex. The rays or line segments are typically referred to as the sides of the angle.
Angles are usually measured in degrees or radians, with a full rotation or circle being 360 degrees or 2π radians. Angles can be classified into different types based on their degree of rotation, such as acute angles, which are less than 90 degrees, right angles, which are exactly 90 degrees, obtuse angles, which are greater than 90 degrees but less than 180 degrees, and straight angles, which are exactly 180 degrees.
Angles can be added, subtracted, multiplied, and divided, and they can be used to solve a wide range of problems in geometry and trigonometry. For example, angles are used to calculate the measurements of geometric shapes, such as triangles, circles, and polygons, and they are also used to calculate distances and heights using trigonometric functions such as sine, cosine, and tangent.
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Sloan Transmissions, Inc., has the following estimates for its new gear assembly project: price = $1,700 per unit; variable costs = $480 per unit; fixed costs = $4.1 million; quantity = 95,000 units. Suppose the company believes all of its estimates are accurate only to within :t15 percent. What values should the company use for the four variables given here when it performs its best- case scenario analysis? What about the worst-case scenario?
Answers
The company should use the following values: Price per unit = $1,445; Variable costs per unit = $552; Fixed costs = $4.715 million ; Quantity = 95,000 units.
what is variables ?In algebra, a symbol (typically a letter) is used to represent an undetermined quantitative score in an expression or algebraic expression. Simply put, a variable is a number that may be changed yet remains fixed. Categorical and numeric variables are the two main types of variables. Then, discrete or continuous categories are made for each category for numerical and categorical variables, respectively. An overview of various types is given in this section. a metric that has a wide range of possible values. Something that can change; a variable's sign; an element of a science experiment that could vary.
To perform a best-case and worst-case scenario analysis, we need to adjust the estimates for each variable based on the given percentage error of 15%.
Best-case scenario analysis:
Price per unit = $1,700 + (15% x $1,700) = $1,955
Variable costs per unit = $480 - (15% x $480) = $408
Fixed costs = $4.1 million - (15% x $4.1 million) = $3.485 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Worst-case scenario analysis:
Price per unit = $1,700 - (15% x $1,700) = $1,445
Variable costs per unit = $480 + (15% x $480) = $552
Fixed costs = $4.1 million + (15% x $4.1 million) = $4.715 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Therefore, for the best-case scenario, the company should use the following values:
Price per unit = $1,955
Variable costs per unit = $408
Fixed costs = $3.485 million
Quantity = 95,000 units
And for the worst-case scenario, the company should use the following values:
Price per unit = $1,445
Variable costs per unit = $552
Fixed costs = $4.715 million
Quantity = 95,000 units
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(1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
Answers
The value of simplification is 95.
What is simplification?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.
Here, we have
Given: (1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
we have to simplify the given expression.
= (1000y) -1/2 * (3/x+1)
When x = 1/3 and y = 1/10
Now we put the value of x and y in the given equation and we get
= (1000/10) -1/2 × (3×3+1)
= 100 - 10/2
= 100 - 5
= 95
Hence, the value of simplification is 95.
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Find the interest on deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016
Answers
The simple interest on a deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016 is given as follows:
$7.4.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The interest accrued is modeled as follows:
I(t) = Prt.
The parameter values for this problem are given as follows:
P = 3650.r = 0.1.t = 74/365 -> there are 74 days from Jan 3 2016 to March 17 2016.Then the interest accrued is given as follows:
I = 365 x 0.1 x 74/365
I = $7.4.
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100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answers
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
(+2).(-4).(-1).(+7)=
(-5).(-6).(+3)=
Answers
Answer:
4 and the second one -8
Step-by-step explanation:
in the first one you have to 2 and take away 4 so you get a negative number and the you take one more number and then add 7
in the second one you have -5 and then take away 6 and then add 3
Please help with this
Answers
please answer it asap.
Answers
Answer:
8^2
Step-by-step explanation:
A pool can be filled by one pipe in 4 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill the pool?
Answers
Step-by-step explanation:
Rate A = 1 pool / 4 hrs = 1/4 pool/hr
Rate B = 1 pool / 5 hrs = 1/5 pool / hr
Now combine the rates to fill 1 pool
1 pool / ( 1/4 pool/hr + 1/5 pool / hr) = 1 / ( 1/4 + 1/5) hr = 2.22 hrs
( or 2 hrs 13.3 min)
The cost of renting a chain saw is $3.90 per hour plus $6.50 for a can of gas. Find the cost of using the chain saw for 7.5 hours.
Equation and Answer
Answers
Answer:
$35.75----------------------------
The total cost is the cost for a can of gas plus rental cost per number of hours.
So the total cost is:
6.50 + 7.5*3.90 = 6.50 + 29.25 = 35.75for both of these graphs i need help finding the equations of the functions
also need help describing the transformation from its parent function (both graphs)
(120 points)
Answers
The equations of the transformed graphs are f(x) = -√(x - 2) and f(x) = -(x + 3)² - 1, while the descriptions are added below
How to describe the functions from the parent function and the equationGraph 1
This function is a square root function
The parent function is the square root function, which is denoted as
f(x) = √x
The function is first reflected across the x-axis to give
f(x) = -√x
Next, the function is shifted to the right by 2 units
So, we have
f(x) = -√(x - 2)
This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the right by 2 units
Graph 2
This function is a quadratic function
The parent function is the square root function, which is denoted as
f(x) = x²
The function is first reflected across the x-axis to give
f(x) = -x²
Next, the function is shifted down and left by 1 and 3 units respectively
This means that
f(x) = -(x + 3)² - 1
This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the down and left by 1 and 3 units
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please help me on this question
Answers
Answer:To calculate how much money Evie will owe after 12 years, we need to use the formula:A = P(1 + r)^nWhere:
A = the amount owed after n years
P = the initial amount borrowed
r = the annual interest rate as a decimal
n = the number of yearsIn this case, P = £600, r = 24% = 0.24, and n = 12. Plugging these values into the formula, we get:A = 600(1 + 0.24)^12
A = 600(1.24)^12
A = 600(7.8905)
A = £4,734.30 (rounded to the nearest penny)Therefore, after 12 years, Evie will owe approximately £4,734.30
Step-by-step explanation: I Helped you Can You help me
What is 2/3 of a full rotation
Answers
Answer:
240°
Step-by-step explanation:
A full rotation is 360°
2/3 x 360 = 240
Helping in the name of Jesus.
Friends ordered a large circular pizza of a certain diameter, however the diameter of the baked pizza was 10% smaller than the one ordered. By the way percentage of the area of the cooked pizza is smaller than the one ordered?
Answers
Answer:
19% smaller
Step-by-step explanation:
A=πr^2
r=d/2
A=pi(d/2)^2
A=pi(.9d/2)^2=
81% of original
100%-81%=19%=Give this answer a like!
please help…………………………….
Answers
The shaded area above the line y = -x + 3 and below the line -2x + y = -1 is the solution region of the system that is option A.
What is graph?A graph is a visual representation of data or mathematical concepts. It is a diagram that shows how variables or quantities relate to each other, often using points, lines, bars, or other symbols. In mathematics, a graph can be used to represent a set of points or a function, where the x-axis represents the input values and the y-axis represents the output values. A graph can show the shape of a function, its range, its domain, and other important features.
Here,
To graph the system, we can first graph the boundary lines of the two inequalities.
For the first inequality, y > -x + 3, we can draw the line y = -x + 3 and shade the area above the line. This is because the inequality is y > -x + 3, which means that all points above the line satisfy the inequality.
Next, for the second inequality, -2x + y < -1, we can draw the line -2x + y = -1 and shade the area below the line. This is because the inequality is -2x + y < -1, which means that all points below the line satisfy the inequality.
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find the length of BC
Answers
The length of line BC as shown in the diagram below is 5√3.
What is length?
Length is the distance between two points.
To calculate the length of Line BC, we use the formula below.
Formula:
BC = AC×sin∅............................... Equation 1Where:
∅ = Angle facing line BCFrom the diagram,
Given:
AC = 10∅ = 60°Sin60° = √3/2Substitute these values into equation 1
BC = (10×√3/2)BC = 5√3Hence, BC is 5√3.
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the area of a table top is a whole number of square feet. Could the length and width be decimal numbers each one with decimal place?
Answers
Yes, the length and width can be decimal numbers each one with decimal place, but not in every case.
Define areaThe size of a two-dimensional surface or region is expressed in terms of area. Square units like square inches, square feet, or square metres are frequently used to measure it. The area of a shape or region is determined by counting the number of unit squares that can fit inside it without overlap.
for example, lets take length =2.5 feet
and width=3.2 feet
area of table top=8 feet²
Taking another case:
length =1.2 feet
and width=3.5 feet
area of table top=4.2 feet²
if the length and width are decimal numbers, then the area would also be a decimal number or whole number, But, this is not possible in every cases.
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The complete question is:
The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.
Please Hurry!!
Which polar coordinates represent the point plotted on the graph? Select all that apply and explain your answer.
Answers
Answer:
D
[tex]3. \frac{11\pi}{6} [/tex]
Step-by-step explanation:
When we determine the point's coordinates, first we have to write the polar ones (they are on the horizontal line) and then the south ones (they are around the circle)
I think this is the right answer
6. Find the first three terms of the expansion of the following in acceding powers of
x
2
1
2
x
x
Answers
The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
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can somebody please help me with these problems !
Answers
Answer:
divide figure in many parts.
Then, find volume of each divided figure :- v= l*b*h
Then add volume of all divided figure
A cup of water holds about 8 ounces is a recipe calls for 1/3 cup of water which is the best estimate of the number of ounces that are needed draw a bar diagram if necessary
Answers
Answer:
One-third cup of water is equivalent to approximately 2.67 ounces (8 ounces divided by 3).
Here is a bar diagram to illustrate this:
|
|
|
|
|
|
|
|______
2.67 oz
In this diagram, the vertical line represents the total amount of water in the cup (8 ounces), and the shaded portion represents the 1/3 cup of water needed for the recipe, which is approximately 2.67 ounces.
Answer:
1/3 cup is approximately equal to 2.67 ounces
Explanation:
In cooking and baking, recipes often use measurements that are different from the standard units of measurement used in daily life. One such measurement is the cup, commonly used to measure liquids like water, milk, and oil. A cup of water typically equals 8 fluid ounces in the United States.
If a recipe calls for 1/3 cup of water, we need to convert this measurement into ounces to know how much water is needed. To do this, we can use the fact that 1 cup is equal to 8 ounces.
To convert 1/3 cup to ounces, we can multiply the number of cups by the number of ounces in one cup. That is:
1/3 cup * 8 ounces/cup = 8/3 ounces
However, 8/3 ounces is not a convenient number to work with, so we need to round it to a more practical value. One reasonable approximation for 8/3 is 2.67. Therefore, we can say that 1/3 cup equals approximately 2.67 ounces.
This approximation is reasonable because it is close to the exact value of 8/3 ounces. Using 2.67 ounces as an estimate for 1/3 cup of water in a recipe should provide a good approximation of the water needed.
noah is filling a tank with water at a constant rate of 0.5 gallons per minute. what is the rate of filling in minutes per gallon?
Answers
Noah is consistently adding 0.5 gallons of water every minute to a tank. 2 minutes are spent filling a gallon.
The rate of filling is the amount of water that is filled per unit of time. In this instance, Noah is consistently adding 0.5 gallons of water each minute to the tank.
To determine the rate of filling in minutes per gallon, we can simply take the reciprocal of the rate of filling in gallons per minute.
That is:
Rate of filling in minutes per gallon = 1 / Rate of filling in gallons per minute
So, the rate of filling in minutes per gallon is:
1 / 0.5 gallons per minute = 2 minutes per gallon
Therefore, Noah is filling the tank at a rate of 2 minutes per gallon.
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3. Create a graph that shows three linear relationships with different y-intercepts using
the following slopes, and write an equation for each line.
Slopes:
●
5/5 5/5 115
3
y
Answers
Setting x = 0, we get the y-intercept: y = 31/5. So, the equation of the line is y = 6/5x + 31/5.
What does line intersect?In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.
by the question.
To find different y-intercepts using the given slopes, we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. To find the y-intercept, we can set x = 0 and solve for y.
For slope 1/5, let's choose the point (2, 3) on the line. Using the point-slope form, we get:
y - 3 = 1/5(x - 2)
y - 3 = 1/5x - 2/5
y = 1/5x + 13/5
Setting x = 0, we get the y-intercept: y = 13/5. So, the equation of the line is y = 1/5x + 13/5.
For slope 3/5, let's choose the point (4, 2) on the line. Using the point-slope form, we get:
y - 2 = 3/5(x - 4)
y - 2 = 3/5x - 12/5
y = 3/5x + 8/5
Setting x = 0, we get the y-intercept: y = 8/5. So, the equation of the line is y = 3/5x + 8/5.
For slope 6/5, let's choose the point (-1, 5) on the line. Using the point-slope form, we get:
y - 5 = 6/5(x + 1)
y - 5 = 6/5x + 6/5
y = 6/5x + 31/5
To learn more about point-slope:
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