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

User Filur
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1 Answer

24 votes
24 votes

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

User Danny Allen
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2.5k points