For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 8.4 x + 8.1 y = 8.7 and 8.1 x - 8.4 y = 2.1
A) parallel lines
B) lines that intersect but are not perpendicular
C) perpendicular lines

Question

Quizplus · Accepted Answer

To determine if the lines are parallel or perpendicular, we can find the slopes of both lines by putting them in slope-intercept form (y = mx + b).
8.4 x + 8.1 y = 8.7
8.1 y = -8.4 x + 8.7
y = (-8.4/8.1) x + (8.7/8.1)
y = -1.037 x + 1.074
So the slope of the first line is -1.037.
8.1 x - 8.4 y = 2.1
-8.4 y = -8.1 x + 2.1
y = (8.1/8.4) x - (2.1/8.4)
y = 0.9643 x - 0.25
So the slope of the second line is 0.9643.
Two lines are perpendicular if and only if the product of their slopes is -1.
(-1.037) * (0.9643) = -1.000008999 ~ -1
Therefore, the lines are perpendicular.

For the Following Pair of Equations, Predict Whether They Represent