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
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.
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.
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)
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