Question

How do you write an equation in point-slope form for the given (–2, 1) and (4, 13)?

Answer 1

Use the slope formula to find slope `m = 2`, then use the second point to get:

`y - 13 = 2(x - 4)`

Explanation:

Given two points `(x_1, y_1)` and `(x_2, y_2)`, then the slope `m` of a line through those two points is given by the formula:

`m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)`

In our case, let `(x_1, y_1) = (-2, 1)` and `(x_2, y_2) = (4, 13)`. Then:

`m = (13 - 1) / (4 - (-2)) = 12 / 6 = 2`

Then point slope form for a line is:

`y - y_0 = m(x - x_0)` where `m` is the slope and `(x_0, y_0)` is some point on the line. To avoid double minus signs, let's use the second point `(4, 13)` to get:

`y - 13 = 2(x-4)`