Answer
Perpendicular
Work Step by Step
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.
