Question

Determine if the two lines with equations 3y+12x = -9 and 2y = 8x+10 are parallel, perpendicular, or neither.

a) not enough information
b) neither
c) parallel
d) perpendicular

Answer 1

After converting both equations into slope-intercept form, we find the slopes to be -4 and 4, which are negative reciprocals of each other. Hence, the two lines with equations 3y + 12x = -9 and 2y = 8x + 10 are perpendicular to each other. So, the correct answer is option d.

Step-by-step explanation:

To determine if two lines with equations 3y + 12x = -9 and 2y = 8x + 10 are parallel, perpendicular, or neither, we need to find the slopes of both lines. For two lines to be parallel, their slopes must be equal. For two lines to be perpendicular, the product of their slopes must be -1.

First, let's put both equations in the slope-intercept form (y = mx + b), where 'm' represents the slope:

1. For 3y + 12x = -9, dividing the entire equation by 3 yields y = -4x - 3. So, the slope (m) of the first line is -4.
2. For 2y = 8x + 10, dividing the entire equation by 2 yields y = 4x + 5. Thus, the slope (m) of the second line is 4.

Since the slopes are negative reciprocals of each other, the two lines are perpendicular, forming a 90° angle between each other. Therefore, the correct answer is (d) perpendicular.