Final answer:
To determine if the lines 2x + 4y = 32 and y = -12x + 16 are parallel, perpendicular, or neither, we compare their slopes. The slopes are -1/2 and -12 respectively. Since these slopes are neither negative reciprocals nor equal, the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To determine the relationship between the two given lines, we need to look at their slopes. The slope of a line in the form ax + by = c can be found by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope.
The first line can be rearranged as follows:
2x + 4y = 32
4y = -2x + 32
y = (-1/2)x + 8
The slope of the first line is -1/2.
The second line is already in slope-intercept form:
y = -12x + 16
The slope of the second line is -12.
If two lines are perpendicular, the product of their slopes should be -1. The product of the slopes of our lines is (-1/2) * (-12) = 6, which is not equal to -1, therefore the lines are not perpendicular. Since their slopes are also not equal, the lines are not parallel. So our answer is:
c) Neither parallel nor perpendicular