Question

write an equation that represents the line. (-3,-6) and (2,-2) use exact numbers

Answer 1

Given:

The line passes through (-3,-6) and (2,-2).

To find:

The equation of line.

Solution:

If a line passes through two points $(x_1,y_1)\text{ and }(x_2,y_2)$, 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 (-3,-6) and (2,-2). So, the equation of line is

$y-(-6)=\dfrac{-2-(-6)}{2-(-3)}(x-(-3))$

$y+6=\dfrac{-2+6}{2+3}(x+3)$

$y+6=\dfrac{4}{5}(x+3)$

$y+6=\dfrac{4}{5}(x)+\dfrac{4}{5}(3)$

Subtract 6 from both sides.

$y=\dfrac{4}{5}(x)+\dfrac{12}{5}-6$

$y=\dfrac{4}{5}(x)+\dfrac{12-30}{5}$

$y=\dfrac{4}{5}(x)+\dfrac{-18}{5}$

$y=\dfrac{4}{5}(x)-\dfrac{18}{5}$

Therefore, the equation of line is $y=\dfrac{4}{5}(x)-\dfrac{18}{5}$.