Find an equation for the line that passes through the points (-6,-6) and (2,-4) .

Answer 1

Hello, thank you for taking the time to post your question!

The underlying equation that you’re trying to find here is y = mx + b, so in order to find that we need to locate the values of both the slope(m) and the y-intercept(b)

m = (y2 – y1) / (x2 – x1) = (-4 - -6) / (2 - -6) = 2 / 8 = 0.25

so that means the general form is at y = 0.25x + b

the final step then is to use one of the points to find the y-intercept

-4 = 0.25(2) + b

-4 = 0.50 + b

-4.5 = b

Putting it all together then gives us the final equation

y = 0.25x – 4.5

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Slope is Δy/Δx, or rise/run, or (y₂ - y₁)/(x₂ - x₁) → (-4 - -6)/(2 - -6) = 2/8 = 1/4 = m

y = mx + b

-4 = (1/4)(2) + b (Using point (2,-4))

-4 = 1/2 + b

b = -4 1/2

y = (1/4)x - 4 1/2

Answer 3

Use two-point form:

(y + 6) / (x + 6) = (-4 + 6) / (2 + 6)

Answer 4