## Precalculus: Mathematics for Calculus, 7th Edition

These two lines are $\textbf{parallel}$
$2x-3y=10$ $;$ $3y-2x-7=0$ Solve $2x-3y=10$ for $y$: $2x-3y=10$ $3y=2x-10$ $y=\dfrac{2}{3}x-\dfrac{10}{3}$ Solve $3y-2x-7=0$ for $y$: $3y-2x-7=0$ $3y=2x+7$ $y=\dfrac{2}{3}x+\dfrac{7}{3}$ Both equations are now in slope-intercept form, which is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept. From the equations, it can be identified that both slopes are $m=\dfrac{2}{3}$ Since the slopes of both lines are equal, these two lines are $\textbf{parallel}$