The slope of a line through the points (-2, 4) and (6, b) is - \frac-{3}{4} What is the value of b? Explain your method for calculating b.

Question

The slope of a line through the points (-2, 4) and (6, b) is -
`\frac-{3}{4}` What is the value of b? Explain your method for calculating b.

Answer 1

b = -2

Explanation:

Answer 2

Answer: b = -2

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Work Shown:

m = (y2-y1)/(x2-x1)

m = (b-4)/(6-(-2))

m = (b-4)/(6+2)

m = (b-4)/8

Set this equal to the slope -3/4 and solve for b

(b-4)/8 = -3/4

4*(b-4) = 8*(-3) ... cross multiply

4b-16 = -24

4b = -24+16 ... adding 16 to both sides

4b = -8

b = -8/4

b = -2

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Since b = -2, we can replace b with -2

That makes the point (6,b) turn into (6,-2)

Now apply the slope formula to (-2,4) and (6,-2). We should get -3/4 as a result

m = (y2-y1)/(x2-x1)

m = (-2-4)/(6-(-2))

m = (-2-4)/(6+2)

m = -6/8

m = -3/4

So everything works out.