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if points are (4,a) and (8,3a) and the slope is 1/3 what is a?

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2 Answers

Use the slope formula: m = (y2 - y1)/(x2 - x1). In this case:

     x1 = 4, y1 = a, x2 = 8, y2 = 3a

so plug in:

     m = (3a - a)/(8 - 4) = 2a / 4

But since 2a/4 = 1/3, cross-multiply and solve the proportion. You get

     6a = 4, so

a = 4/6 = 2/3

 

You are given two points on a line:

     point 1  ==>  (x1, y1) = (4, a)  ==>  where x1 = 4 and y1 = a

     point 2  ==>  (x2, y2) = (8, 3a)  ==>  where x2 = 8 and y2 = 3a 

You are also given that the slope (m) of this line that passes thru these points is 1/3. That is,  m = 1/3.

Recall that the formula for the slope of a line that passes through any two points (x1, y1) and (x2, y2) is:

     m = (y2 - y1) / (x2 - x1

Thus, for the slope of the line that passes through the two points given above we find that:

     1/3 = (3a - a) / (8 - 4)

      1/3 = (2a) / (4)

     1/3 = a/2

Multiplying both sides of the equation by 2, we solve for a:

            1/3 = a/2

      2*(1/3) = 2*(a/2)

           2/3 = a