Question

Graph the line that passes through the points (-5,3) and (-1,-1) and determine the equation of the line

Answer 1

We are to find the equation of a line passing through the points

$\begin{gathered} (-5,\text{ 3) and (-1, -1) } \\ \end{gathered}$

Here

$\begin{gathered} x_1=-5,x_2=\text{ -1} \\ y_1=3,y_2=\text{ -1} \end{gathered}$

The formula for the equation of a line passing through two points is given as

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

Substituting values we get

$\begin{gathered} \frac{y\text{ - 3}}{x\text{ - (-5)}}\text{ = }\frac{-1\text{ -3}}{-1\text{ - (-5)}} \\ \frac{y\text{ - 3}}{x\text{ + 5}}\text{ = }\frac{-4}{-1\text{ + 5}} \\ \frac{y\text{ - 3}}{x\text{ + 5}}\text{ = }\frac{-4}{4} \\ \frac{y\text{ - 3}}{x\text{ + 5}}\text{ = -1} \\ \text{cross multiplying} \\ y\text{ - 3 = -1(x + 5)} \\ y\text{ - 3 = -x -5} \\ y\text{ = -x -5 + 3} \\ y\text{ = -x - 2} \\ y\text{ + x = -2} \end{gathered}$

Therefore the equation of the line is y + x = -2

Plotting the graph