Equation of a line through (-1, -6) and (3, 8)

Answer 1

Hi Kels!

You'll need three formulas for this problem: calculating slope, Point-Slope Formula, and Slope-Intercept form.

We calculate slope (m) with the equation m = (y_{2 -} y₁)/(x₂ - x₁)

For these problems, you just have to assign one ordered pair as 1 (x₁, y₁) and the other as 2 (x₂, y₂).

For this one, let's say that (-1, -6) is ordered pair 1 (x₁, y₁) and (3, 8) is ordered pair 2 (x₂, y₂).

Plugging this into our slope formula, we get m = (8 -[-6]) / (3 -[-1]) *remember that when we subtract a negative, it's like adding a positive!*

We simplify that equation into ---> m = (8 + 6) / (3 + 1)

m = (14) / (4) ---> since this cannot be divided into a whole number, we'll simplify our fraction into m = 7/2.

Now! We're going to take that slope (m = 7/2) and plug that into the Point-Slope Formula

y - y₁ = m(x - x₁) Remember here we already assigned (-1, -6) as ordered pair 1 (x₁, y₁).

y - (-6) = (7/2)(x - [-1])

y + 6 = (7/2)(x + 1) Distribute the 7/2 to both x and 1

y + 6 = (7x/2) + (7/2) Now we solve for y to get to slope-intercept form (y = mx + b)

-6 - 6

y = (7x/2) - (5/2)

And that's your answer!

to make it clear how to write the answer, here is how it should look. Hope this helps! :)

y = 7x - 5

2 2

Answer 2

Use two-point form

(y + 6) / x + 1) = (-6 - 8) / (-1 - 3)