Use the Slope–Intercept Form of an Equation of a Line: example 4.51

Use slopes and y-intercepts to determine if the lines $3 x - 2 y = 6$ and $y = \frac{3}{2} x + 1$ are parallel.

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 $2 x + 5 y = 5 and y = - \frac{2}{5} x - 4$ are parallel.

How did it go?

Solve the first equation for $y$ .	$\begin{matrix} 3 x - 2 y & = & 6 \\ - 2 y & = & −3 x + 6 \\ \frac{−2 y}{−2} & = & \frac{−3 x + 6}{−2} \end{matrix}$	and	$y = \frac{3}{2} x + 1$
The equation is now in slope-intercept form.	$y = \frac{3}{2} x - 3$
The equation of the second line is already in slope-intercept form.			$y = \frac{3}{2} x + 1$
Identify the slope and $y$ -intercept of both lines.	$\begin{matrix} y & = & \frac{3}{2} x - 3 \\ y & = & m x + b \\ m & = & \frac{3}{2} \end{matrix}$		$\begin{matrix} y = \frac{3}{2} x + 1 \\ y = m x + b \\ m = \frac{3}{2} \end{matrix}$
	$y -intercept is (0, −3)$		$y -intercept is (0, 1)$

Solve the first equation for $y$ .	$\begin{matrix} 3 x - 2 y & = & 6 \\ - 2 y & = & −3 x + 6 \\ \frac{−2 y}{−2} & = & \frac{−3 x + 6}{−2} \end{matrix}$	and	$y = \frac{3}{2} x + 1$
The equation is now in slope-intercept form.	$y = \frac{3}{2} x - 3$
The equation of the second line is already in slope-intercept form.			$y = \frac{3}{2} x + 1$
Identify the slope and $y$ -intercept of both lines.	$\begin{matrix} y & = & \frac{3}{2} x - 3 \\ y & = & m x + b \\ m & = & \frac{3}{2} \end{matrix}$		$\begin{matrix} y = \frac{3}{2} x + 1 \\ y = m x + b \\ m = \frac{3}{2} \end{matrix}$
	$y -intercept is (0, −3)$		$y -intercept is (0, 1)$