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

`(y-y_1)/(x-x_1)\text{ = }(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{ = }(-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