Question

Determine the equation of the line that passes through the points (0,−10) and (−8,1).

Answer 1

Solution:

Given the points below;

$\left(0,−10\right)\text{ }and\text{ }(−8,1)$

To find the equation of the line that passes through the points, we will apply the formula below

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Where

$\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-8,1) \end{gathered}$

Substitute the values of the coordinates into the formula above

$\begin{gathered} \frac{y-(-10)}{x-0}=\frac{1-(-10)}{-8-0} \\ \frac{y+10}{x}=\frac{1+10}{-8} \\ \frac{y+10}{x}=-\frac{11}{8} \\ Crossmultiply \\ 8(y+10)=-11(x) \\ 8y+80=-11x \\ 11x+8y+80=0 \end{gathered}$

Hence, the equation of the line is

$11x+8y+80=0$

The graph is shown below with the points indicated using a graphing tool