Question

2. A line goes through the points (8, 9) and (-2, 4).

(a) What is the slope of the line? Show all steps of your work as evidence of the solution.
(b) Write the equation of the line in point-slope form. Show all steps of your work as evidence of the solution.
(c) Write the equation of the line in slope-intercept form. Show all steps of your work as evidence of the solution.

Answer 1

Explanation:

A line goes through the points (-2, 4) and (8, 9). We see that x increases by 10 and y increases by 5.

Thus, the slope of this line is m = rise / run = 5/10 = 1/2 (the slope)

Starting with the point slope equation y - k = m(x - h) and substituting 9 for y, 8 for x and 1/2 for m, we get:

y - 9 = (1/2)(x - 8) (point-slope form)

y = (1/2)x + 5 (slope-intercept form)