## Intermediate Algebra (6th Edition)

We are given two equations of lines. We can transform these equations into the form y=mx+b, where m is the slope of the line and the point (0,b) is the y-intercept. $-2x+3y=1$ Add 2x to both sides. $3y=2x+1$ Divide both sides by 3. $y=\frac{2}{3}x+\frac{1}{3}$ Next, $3x+2y=12$ Subtract 3x from both sides. 2y=−3x+12 Divide both sides by 2. $y=-\frac{3}{2}x+6$ These lines have a different value for m, so they cannot be parallel, as they do not have the same slope. Two lines are perpendicular if the product of their slopes is equal to -1. $\frac{2}{3}\times-\frac{3}{2}=-1$ Therefore, these lines are perpendicular.