Question

A. Find the slope of the line that passes through the points (2,-5) and (-2,3).

b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.

Answer 1

PART A:

Solve for the slope by solving change in y over change in x. We have (3-(-5)/(-2-2) = 8/-4=-2

PART B:

Change in to y=mx+b: -5y = -2x-10. Divide all terms by -5: y = 2/5x + 2. The slope is 2/5 and the y-intercept is 2.

PART C:

Remembering from part a that m=change in y/change in x, we have the equation: -4=1-(-9)/0-x. If we simplify, we have -4=10/0-x. If we multiply both sides from 1/10 we have: -2/5 = -x. So, x = 2/5.

PART D:

We can use point-slope form first:

y-5=-7(x+1). Then we solve the equation! y-5 = -7x-7. After adding 5 to both sides, we have the equation: y=-7x-2.