Question

The vertices of a quadrilateral are A(-1,1), B(2,4), C(2,-4), and D(0,-2), how do you write an equation for the line through A and B?

Answer 1

The equation of the line through `A` and `B` is `y=x+2`.

Explanation:

Find an equation of the line through `A(-1,1)` and `B(2,4)`.

First, find the slope `m` using the slope formula where
`(x_1,y_1)` and `(x_2,y_2)` are points.

`m=frac{y_2-y_1}{x_2-x_1}`

`m=frac{4-1}{2- -1}= 3/3=1`

Next, use the point slope formula of a line where
`m=` the slope and `(x_1,y_1)` is a point. You can choose either point `A` or `B`. I will choose `B` because the math is a bit easier if you have a point with only positive numbers.

`y-y_1=m(x-x_1)`

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

`y-4=x-2`
`color(white)(a)+4color(white)(aaaa)+4`

`y=x+2`