Question

A line passes through the point (4,-2),(9,-8).Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form

Answer 1

First find the slope of the line segment joining (4,-2) and (9,-8). It is:
-8+2 -6
m = -------- = ------
9-4 5

Using slope-intercept form, y = mx + b:

-8 = (-6/5)(9) + b, or -8 = -54/9 + b.

Then b must be -8 = -54/9 + b. Solve for b:

-72 54 -18
----- - ----- = -------- = -2. Then y = mx + b becomes y = (-6/5)x - 2 (slope-
9 9 9 intercept form).

Point-slope form is y-k = m(x-h), where (h,k) is a point on the line.

Then y - (-8) = (-6/5)(x-9). This is in point-slope form.