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

y = –2/3x + 1

2x – 3y = –3

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

y = –2/3x + 1

2x – 3y = –3

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Erik M. | Cabell-Huntington Math TutorCabell-Huntington Math Tutor

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.

Kevin S. |

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.

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## Comments

the first equation is in slope-intercept form, y = mx + b, where slope = m = -2/3; in the second equation, solve for y to put that equation in slope-intercept form also: -3y = -2x - 3; y = (2/3)x + 1; so that the slope for the second line is m = 2/3, which is neither the same slope as for the first equation, nor the negative reciprocal, -3/2, of the slope of the first equation; so that the two lines are neither parallel (equal slopes) nor perpendicular (slopes of two lines are negative reciprocals of one another)