4x-6y=12 and 3x+2y=10 is the equation perpendicular, parallel or neither

Answer 1

Slopes of 2 lines are parallel if the slopes are equal to one another, perpendicular if the slopes are negative reciprocals (ex. -1/4 and 4 or -2 and 1/2) and if neither of these 2 rules are true, then the slopes are neither.

The first step for this problem is to put the equations in slope intercept form to easily see the slope. This means solve each equation for y=.

4x-6y=12

-6y=-4x+12

y=2/3x-2. so the slope if the first equation is 2/3

3x+2y=10

2y=-3x+10

y=-3/2x+5. so the slope of the second equation is -3/2

these are negative reciprocals so the 2 lines are perpendicular