Question

Find the equation of the line passing through the points$P(5,1)$ and $Q(1,-1)$.

Answer 1

Step 1: Solve for slope of the line

Given points are $P(5,1)$ and$Q(1,-1)$

we know that the slope of a line $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the values of $x_1=5,y_1=1,x_2=1,y_2=-1$

$\Rightarrow m=\frac{-1-1}{1-5}=\frac{-2}{-4}=\frac{1}{2}$

Step 2: Solve for equation of line

The equation of the line passing through the points $P(x_1,y_1)$with slope $m$ is $(y-y_1)=m(x-x_1)$

As the line passes through the points$P(5,1)$

$$\begin{gathered} \Rightarrow y-1=\frac{1}{2}(x-5) \\ \Rightarrow 2y-2=x-5 \\ \Rightarrow x-2y-3=0 \end{gathered}$$

Hence the equation of line passing through the points$P(5,1)$ and $Q(1,-1)$is $x-2y-3=0$