Question

Determine the equation of the line that passes through the points (-1 , 10) and (2,4)

Answer 1

Given:

The two points are (-1,10) and (2,4).

To find:

The equation of line which passes though the given points.

Solution:

If a line passes through two points, then the equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through (-1,10) and (2,4). So, the equation of line is

$y-10=\dfrac{4-10}{2-(-1)}(x-(-1))$

$y-10=\dfrac{-6}{2+1}(x+1)$

$y-10=\dfrac{-6}{3}(x+1)$

$y-10=-2(x+1)$

Using distributive property, we get

$y-10=-2x-2$

Adding 10 both sides, we get

$y=-2x-2+10$

$y=-2x+8$

Therefore, the required equation of line is $y=-2x+8$.