Question

Find the equation of the line passing through points (-4,2) and (1,-6)

Answer 1

y + 6 = (-8/5)(x - 1) in point-slope form

Explanation:

Moving from the 1st point to the first, we see that x (the 'run') increases by 5 from -4 to 1, and y (the 'rise') decreases by 8. Thus, the slope of the line through these two points is m = rise / run = -8/5

Now we have two points on the line, plus the slope. Let's write out the point-slope formula for the equation of a straight line:

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

Here, using the point (1, -6), we obtain:

y + 6 = (-8/5)(x - 1) in point-slope form