For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 2.1 x + 9.4 y = 3.9 and 9.4 x - 2.1 y = 8.6
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 need to compare the slopes. In both equations, we can solve for y to get the form y = mx + b, where m is the slope.

For the first equation,

2.1x + 9.4y = 3.9

9.4y = -2.1x + 3.9

y = (-2.1/9.4)x + 3.9/9.4

So the slope of this line is -2.1/9.4.

For the second equation,

9.4x - 2.1y = 8.6

-2.1y = -9.4x + 8.6

y = (9.4/2.1)x - 8.6/2.1

So the slope of this line is 9.4/2.1.

To determine if the lines are perpendicular, we need to check if their slopes are negative reciprocals, meaning their product is -1.

(-2.1/9.4) * (9.4/2.1) = -1

Since the product is -1, the lines are perpendicular. Therefore, the answer is C) perpendicular lines.

For the Following Pair of Equations, Predict Whether They Represent