Question

Find the equation of the line that passes through the points $(7,0)$ and $(-5,4)$

Answer 1

Step 1: Solve for the slope of line passing through the given points

Given points are $P(7,0)$ and$Q(-5,4)$

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

Substitute the values $x_1=7,x_2=-5,y_1=0,y_2=4$

$\Rightarrow m=\frac{4-0}{-5-7}=\frac{-4}{12}=\frac{-1}{3}$

Step 2: Solve for the equation of line

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

As the line passes through the point $(7,0)$

$$\begin{gathered} \Rightarrow y-0=\frac{-1}{3}(x-7) \\ \Rightarrow -3y=x-7 \\ \Rightarrow x+3y-7=0 \end{gathered}$$

Hence the equation of line passing through the points $(7,0)$ and $(-5,4)$ is $x+3y-7=0$