Question

Find the equation of a line with $x$-intercept = $5$ and passing through the point $(4,-7)$

Answer 1

Equation of line passing through $x$-intercept as $5$ and $(4,-7)$:

Given that , $x$ - intercept is $5$ which can be simply written as $(5,0)$

The line passes through $(5,0)$ and $(4,-7)$:

Equation Of Line Passing Through Two Points:

$\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

From the given points $(5,0)$ and $(4,-7)$ we can write $x_1=5,x_2=4,y_1=0,y_2=-7$

$$\begin{gathered} \text{⇒}\left(y-0\right)=\frac{\left(-7-0\right)}{\left(4-5\right)}\left(x-5\right) \\ \Rightarrow y=\frac{-7}{-1}\left(x-5\right) \\ \Rightarrow y=7(x-5) \\ \Rightarrow y=7x-35 \\ \Rightarrow 7x-y-35=0 \end{gathered}$$

Therefore , the equation of line with $x$-intercept as $5$ and passing through $(4,-7)$ is $7x-y-35=0$.