Tell if the following pair of lines is parallel, perpendicular, or neither.

3x - 2y= 16
y= -2/3x + 4

slope of first line = 3/2

slope of 2nd line = -2/3

draw your conclusion based on what you must have learned about lines and their slopes

neither?

no, they are perpendicular

I one line has a slope of a/b then a perpendicular line has slope of -b/a , that is,
one slope is the opposite reciprocal of the other.

That is the case here: 3/2 vs -2/3

To determine if the pair of lines is parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope.

The first equation, 3x - 2y = 16, can be rearranged into slope-intercept form by isolating y:
-2y = -3x + 16
y = (3/2)x - 8

The second equation, y = (-2/3)x + 4, is already in slope-intercept form.

Comparing the slopes:
The slope of the first equation is 3/2, and the slope of the second equation is -2/3.

If the slopes of two lines are equal, they are parallel. If the slopes are negative reciprocals of each other (i.e., when you multiply one slope by -1 and flip the sign, you get the other slope), then the lines are perpendicular. Otherwise, if the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.

In this case, since the slopes 3/2 and -2/3 are neither equal nor negative reciprocals, the pair of lines is neither parallel nor perpendicular.