Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 30

Determine the equation of the line with $x$-intercept $2$, containing the point $(4,-5)$. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

Since the $x$-intercept is $2, (2,0)$ is a point of the line and $(4,-5)$ is also a point of the line. We can solve for the slope,

$\displaystyle m = \frac{-5-0}{4-2} = \frac{-5}{2}$

Using Point Slope Form,


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&&
\\
\\
y - 0 =& \frac{-5}{2} (x-2)
&& \text{Substitute } m = \frac{-5}{2}, x = 2 \text{ and } y = 0
\\
\\
y =& \frac{-5}{2}x + 5
&& \text{Slope Intercept Form}
\\
\\
5x + 2y =& 10
&& \text{General Form}

\end{aligned}
\end{equation}
$