Question

A line passes through (1, –5) and (–3, 7).Write an equation for the line in point-slope form.

Rewrite the equation in slope-intercept form.

Answer 1

y – 5 = 3(x + 1); y = 3x + 8

Explanation:

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Answer 2

y - 7 = 3(x + 3) and y = 3x + 16

Explanation:

Find the slope first:

As we go from (–3, 7) to (1, –5), x increases by 4 and y increases by 12. Hence, the slope is m = rise / run = 12 / 4, or m = 3.

Next, modify the point-slope form y - k = m(x - h) by inserting the given info:

y - 7 = 3(x -[-3]), or

y - 7 = 3(x + 3)

Note: (h, k) represents the given point, which I have chosen to be (-3, 7).

Next, convert this result to slope-intercept form. Begin by solving this equation for y: y = 7 = 3x + 9, or:

y = 3x + 16