For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 3.8 x + 1.1 y = 8.1 and 1.1 x - 3.8 y = 1.2
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 must first rewrite the equations in slope-intercept form (y = mx + b):
3.8x + 1.1y = 8.1 
1.1y = -3.8x + 8.1 
y = (-3.45)x + 7.36

1.1x - 3.8y = 1.2 
-3.8y = -1.1x + 1.2 
y = (0.29)x - 0.32

Now we can see that the slope of the first equation is -3.45 and the slope of the second equation is 0.29. To determine if the lines are perpendicular, we need to multiply the slopes together, and the result should be -1. 
(-3.45) * (0.29) = -0.999, which is close enough to -1.

Therefore, the two lines are perpendicular.

For the Following Pair of Equations, Predict Whether They Represent