Question

Tell whether the pair of lines are parallel, perpendicular, or neither.
y = 3/4x + 7 and 4x - 3y = 9

Answer 1

To determine whether the pair of lines given by the equations y = 3/4x + 7 and 4x - 3y = 9 are parallel, perpendicular, or neither, we need to compare their slopes.

First, let's write the second equation in slope-intercept form:

4x - 3y = 9
-3y = -4x + 9
y = 4/3x - 3

Now we can compare the slopes of the two lines. The slope of the first line y = 3/4x + 7 is 3/4, and the slope of the second line y = 4/3x - 3 is 4/3.

Since the slopes of the two lines are not the same (3/4 and 4/3 are reciprocals of each other but not equal), we can conclude that the lines are not parallel.

Since the product of the slopes of the two lines is not -1 (3/4 * 4/3 = 1), we can conclude that the lines are not perpendicular.

Therefore, the pair of lines given by the equations y = 3/4x + 7 and 4x - 3y = 9 are neither parallel nor perpendicular.