Example 4.54 from Elementary Algebra, 4.5 Use the Slope–Intercept Form of an Equation of a Line

Use the Slope–Intercept Form of an Equation of a Line: example 4.54

Use slopes and y-intercepts to determine if the lines $y = 2 x - 3$ and $−6 x + 3 y = −9$ are parallel. You may want to graph these lines, too, to see what they look like.

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 and y-intercepts to determine if the lines $y = - \frac{1}{2} x - 1$ and $x + 2 y = 2$ are parallel.

How did it go?

	$y = 2 x - 3$	and	$−6 x + 3 y = −9$
The first equation is already in slope-intercept form.	$y = 2 x - 3$
Solve the second equation for $y$ .			$\begin{matrix} - 6 x + 3 y & = & −9 \\ 3 y & = & 6 x - 9 \\ \frac{3 y}{3} & = & \frac{6 x - 9}{3} \\ y & = & 2 x - 3 \end{matrix}$
The second equation is now in slope-intercept form.	$y = 2 x - 3$
Identify the slope and $y$ -intercept of both lines.	$\begin{matrix} y & = & 2 x - 3 \\ y & = & m x + b \\ m & = & 2 \end{matrix}$		$\begin{matrix} y & = & 2 x - 3 \\ y & = & m x + b \\ m & = & 2 \end{matrix}$
	$y -intercept is (0, −3)$		$y -intercept is (0, −3)$

	$y = 2 x - 3$	and	$−6 x + 3 y = −9$
The first equation is already in slope-intercept form.	$y = 2 x - 3$
Solve the second equation for $y$ .			$\begin{matrix} - 6 x + 3 y & = & −9 \\ 3 y & = & 6 x - 9 \\ \frac{3 y}{3} & = & \frac{6 x - 9}{3} \\ y & = & 2 x - 3 \end{matrix}$
The second equation is now in slope-intercept form.	$y = 2 x - 3$
Identify the slope and $y$ -intercept of both lines.	$\begin{matrix} y & = & 2 x - 3 \\ y & = & m x + b \\ m & = & 2 \end{matrix}$		$\begin{matrix} y & = & 2 x - 3 \\ y & = & m x + b \\ m & = & 2 \end{matrix}$
	$y -intercept is (0, −3)$		$y -intercept is (0, −3)$

Use the Slope–Intercept Form of an Equation of a Line: example 4.54

Solution

Your turn

Use the Slope–Intercept Form of an Equation of a Line: example 4.54

Solution

Your turn