Question

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

Answer 1

Answer:

y - 7 = 3(x + 3)  and  y = 3x + 16

Step-by-step 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