Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

RECALL: (1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$= slope and $(0, b)$ is the line's y-intercept. (2) Parallel lines have the same slope. (3) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write each equation in slope-intercept form by solving for $y$ to obtain: First Equation: $4y+2=3x \\4y+2-2=3x-2 \\4y=3x-2 \\\frac{4y}{4}=\frac{3x-2}{4} \\y=\frac{3}{4}x-\frac{1}{2}$ The slope of this line is $\frac{3}{4}$. Second Equation: $-3x+4y=-12 \\-3x+4y+3x=-12+3x \\4y=-12+3x \\4y=3x-12 \\\frac{4y}{4}=\frac{3x-12}{4} \\y=\frac{3}{4}x-3$ The slope of this line is $\frac{3}{4}$. The two lines have the same slope, so they are parallel.