Question

How do you write the equation of a line given (2,4) (-4,-5)?

Answer 1

We write the equation in 'point-slope' form, so we need to find the y-intercept and the gradient (slope).

The equation of the line is `y=3/2x+1`

Explanation:

We will find the equation of the line in 'point-slope' form:

`y=mx+c` where `m` is the gradient and `c` is the y-intercept.

First we need to find the gradient (slope) of the line:

`m=(y_2-y_1)/(x_2-x_1) = (-5-4)/(-4-2) = (-9)/(-6) = 3/2`

Now we need to find the y-intercept, `c`. (sometimes people call it 'b')

We can choose either of the points we are given to substitute into the equation. Let's choose `(2,4)`.

`y=mx+c`

`4=3/2(2)+c`

`c=1`

Over all, then, the equation of the line is `y=3/2x+1`