Question

Find the equation using the points.

(1/2, -3/2) (-1/2, 1/2)

Answer: y=2x-1/2

Please explain why this is the answer.

Answer 1

If y = mx+b, plug in the points to get

1/2 m + b = -3/2
-1/2 m + b = 1/2
add them together to get
2b = -1
b = -1/2
subtract them to get
m = -2
y = mx+b = -2x - 1/2

or, consider the slope of the line:
(y2-y1)/(x2-x1) = (1/2+3/2)/(-1/2-1/2) = -2
Now use the point-slope form to get
y+3/2 = -2(x-1/2)
y = -2x+1-3/2 = -2x - 1/2

Better check that answer key