Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these.
A)parallel lines
B)perpendicular lines
C)neither

Question

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​   ​
A)parallel lines 
B)perpendicular lines 
C)neither

Quizplus · Accepted Answer

To determine whether the lines are parallel, perpendicular or neither, we need to find the slope (m) for each equation.

For the first equation, we can rewrite it in slope-intercept form as:

-2x - 3y = 6

-3y = 2x + 6

y = (-2/3)x - 2

So the slope for the first equation is -2/3.

For the second equation, we can rewrite it in slope-intercept form as:

3x - 2y = 4

-2y = -3x + 4

y = (3/2)x - 2

So the slope for the second equation is 3/2.

To determine if the lines are perpendicular, we need to check if the product of their slopes is -1:

(-2/3)*(3/2) = -1

Since the product is -1, the lines are perpendicular.

Determine Whether the Following Pairs of Equations Represent Parallel Lines