Question

What is the equation in point-slope form of the line passing through (2, 5) and (–1, 8)?

Answer 1

`y = -x + 7`

Explanation:

First, we have to find the slope of the equation. To find the slope we have to do;

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

For our question slope is;

`m = (8-5)/(-1-2) = 3/-3 = -1`

The equation of a line is;

`y=ax+b`

We should use one point to find the real equation. If we use `(2,5)` point;

`y= ax+b => 5=2a+b`

`a` is the slope of the equation, we found that as `-1`;

`5 = 2 * (-1) + b => 5= -2 +b => b=7`

So the equation of the line will be;

`y=ax+b => y= -x+7`

We can check if our equation is right or not with other given point;

`(-1,8) => y=-x+7 => 8=-(-1)+7 => 8=8`