Question

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

Answer 1

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

`(y-y_1)/(x-x_1)=(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} (y-(-10))/(x-0)=(1-(-10))/(-8-0) \\ (y+10)/(x)=(1+10)/(-8) \\ (y+10)/(x)=-(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