Use the Slope–Intercept Form of an Equation of a Line: example 4.55

Use slopes to determine if the lines, $y = −5 x - 4$ and $x - 5 y = 5$ are perpendicular.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use slopes to determine if the lines $y = −3 x + 2$ and $x - 3 y = 4$ are perpendicular.

How did it go?

The first equation is already in slope-intercept form.	$\begin{matrix} y & = & −5 x - 4 \end{matrix}$
Solve the second equation for $y$ .	$\begin{matrix} x - 5 y & = & 5 \\ - 5 y & = & − x + 5 \\ \frac{−5 y}{−5} & = & \frac{− x + 5}{−5} \\ y & = & \frac{1}{5} x - 1 \end{matrix}$
Identify the slope of each line.	$\begin{matrix} y & = & −5 x - 4 \\ y & = & m x + b \\ m_{1} & = & −5 \end{matrix}$	$\begin{matrix} y & = & \frac{1}{5} x - 1 \\ y & = & m x + b \\ m_{2} & = & \frac{1}{5} \end{matrix}$

The first equation is already in slope-intercept form.	$\begin{matrix} y & = & −5 x - 4 \end{matrix}$
Solve the second equation for $y$ .	$\begin{matrix} x - 5 y & = & 5 \\ - 5 y & = & − x + 5 \\ \frac{−5 y}{−5} & = & \frac{− x + 5}{−5} \\ y & = & \frac{1}{5} x - 1 \end{matrix}$
Identify the slope of each line.	$\begin{matrix} y & = & −5 x - 4 \\ y & = & m x + b \\ m_{1} & = & −5 \end{matrix}$	$\begin{matrix} y & = & \frac{1}{5} x - 1 \\ y & = & m x + b \\ m_{2} & = & \frac{1}{5} \end{matrix}$