Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.

Question

Tell whether the lines for the pair of equations are parallel, perpendicular, or neither

y = –2/3x + 1

2x – 3y = –3

Answer 1

Teri:

Some direction on this:

1 - get both equations into the form y = mx + b (the first one is already there)

2 - Then look at the slope (m):

(a) If the slopes are equal, the lines are parallel

(b) if the slope of one is the negative reciprocal of the other, the lines are perpendicular
Example: the slope of the first equation is -2/3 . For the second equation to be perpendicular to the first, the slope of the second equation would need to be 3/2.

(c) If the slopes are not the same, and one is not the negative reciprocal of the other, then the lines intersect and are neither parallel or perpendicular.

Answer 2

Neither.

Solve for y for the second equation: y = 2/3x + 1

Both equations will cross the y axis at +1, but one will have a slope of 2/3, and one will be -2/3 slope.

A perpindicular line has the negative reciprocal of the slope, not just the negative.