Question

What is the equation of a line, in point-slope form, that passes through (-4, -1) and has a slope of (5, 7)

Answer 1

The point-slope equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope.

slope = m = (y2 - y1)/(x2 - x1) = (-1 - 7)/(-4 - 5) = -8/-9 = 8/9

You can use either point as (x1, y1). I will use point (5, 7).

y - 7 = (8/9)(x - 5)

Answer 2

It is y+1=0.9(x+4) because the formula is y - y1=m(x + x1) you only need one point and the slope. If you have two points, you need to find the slope by using the slope formula slope=y2-y1/x2-x1. Filling it in it would look like slope=7-(-1)/5-(-4). The double negatives cancel each other out and it turns to addition signs leaving us with slope=7+1/5+4 so the slope is 8/9 or 0.9. Now you can fill out the point-slope formula y+1=0.9(x+4)