Write an equation of a line that passes through the points (-2,6) and (-4,14).

Question

I'm not sure how to do this.

Thanks!!

Answer 1

Once you've figured out that the slope is -4, as described in Todd's response, you can enter either of the two given points into the slope-intercept form to solve for b.

y = mx + b -> 6 = -4(-2) + b -> 6 = 8 + b -> b = 6 - 8 = -2

So y = -4x - 2

Would work as well using point (-4, 14). 14 = -4(-4) + b -> 14 = 16 + b, etc.

Answer 2

You can use the two points (-2, 6) or (x₁, y₁) and (-4, 14) or (x₂, y₂) to solve for the slope of the line, using the slope (m) formula:

m = (y₂ -y₁)/(x₂ -x₁) => (14-6)/(-4-(-2)) = 8/(-2) = -4

Then, plug the slope (m) of -4 into the point-slope formula using either of the 2 points given:

y - y₁ = m(x - x₁) => y - 6 = -4(x - (-2)) or y - 6 = -4(x + 2).

This can be re-written in slope-intercept form y = mx + b (where b = y-intercept) by rearranging:

First, distribute -4 across x + 2 => y - 6 = -4x - 8

Then, add 6 to both sides:

y = -4x - 2

Hope this helps,

Todd