Question

How do you write an equation of a line with points (-2,5), (5,-2)?

Answer 1

`y = -x +3`

Explanation:

A line is given by the equation `y - y_0 = m(x-x_0)` where `m` is the slope of the line, and `(x_0,y_0)` a point on the line. To find the slope of a line when two of its points - `(x_1,y_1)` and `(x_2,y_2)` are known, use the formula:

`m = (y_2-y_1)/(x_2-x_1)`

In this case, `m = (-2 - 5)/(5 - (-2)) = -7/7 = -1`.

Let's use the point `(x_1,y_1)` as the point `(x_0, y_0)` from the first equation:

`y - 5 = -1(x-(-2)) => y = -x -2 + 5 => y = -x +3`