College Algebra 7th Edition

RECALL: (1) Parallel lines have equal slopes. (2) Perpendicular lines have slopes whose product is $-1$. (3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope. Write both equations in slope-intercept form to obtain: $\bf\text{Equation 1}:$ $2x-3y=10 \\-3y=-2x+10 \\\dfrac{-3y}{-3} = \dfrac{-2x+10}{-3} \\y = \dfrac{2}{3}x - \dfrac{10}{3}$ $\bf\text{Equation 2}:$ $3y-2x-7=0 \\3y=2x+7 \\\dfrac{3y}{3} = \dfrac{2x+7}{3} \\y=\dfrac{2}{3}x+\dfrac{7}{3}$ The two lines have equal slopes. Thus, the two lines are parallel to each other.