HELP ASAP PLEASE!!!!!!

Answer:

y = x/2

Step-by-step explanation:

y = -x has a negative slope so cross this one out.

y = 2x has a steeper slope that would be above the black line so cross this one out

y = 0.001x has a slope that acends very slowly so cross this one out.

y = x/2 is the best match.

Some terminology:

 ⇒what is the slope

    ⇒ is the steepness of the line

        ⇒calculated by dividing the rise over the run

           ⇒ rise is the change in the y-direction

               ⇒ run is the change in the x-direction

                  ⇒look at the diagram I attached

 ⇒ how to find the slope in a linear equation

     ⇒look to the coefficient of the 'x' variable

        ⇒ that is the slope

      Ex. For the line y = x, the slope is 1

⇒A line with a positive slope rises from left to right while a line with a    negative slope falls from left to right.

   Ex. y=x has a positive slope and thus is rising

We want to find the equation that could represent the blue line

   ⇒ let's look into each equation and see whether they work or not

First case: [tex]y = -x[/tex]

  ⇒The equation given has the line falling, when the graph in the    

  equation is rising

       ⇒ not the answer

Second case: [tex]y=2x[/tex]

   ⇒ the equation given has the line that has a bigger slope than the

  the equation shown, which has a smaller slope than y = x

       ⇒ not the answer

Third case: [tex]y=\frac{1}{2}x[/tex]

    ⇒ the equation given fits the requirement of having a rising slope that

    is smaller than y = x

        ⇒ is a possible answer

Fourth case: [tex]y = 0.001x[/tex]

     ⇒ the equation given has a slope that is almost horizontal when the

     line shown in the graph doesn't

          ⇒ not the answer

Thus after examing all the choices:

   ⇒ Answer: [tex]y=\frac{1}{2}x[/tex]

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