Two lines are parallel if their slopes are equal. The equations of the lines are in the standard form Ax + By = C, where A is the coefficient of x, B is the coefficient of y, and the slope of the line is -A/B.
For the first equation -4 = 3x + 6y, the slope is -3/6 = -1/2.
For the second equation ax - 8y = 12, the slope is -a/8.
To make the slopes equal and have the two lines parallel, we need to set the slopes equal to each other:
-a/8 = -1/2
Multiply both sides by -8 to get a by itself:
a = 4
Therefore, the value of a for the two lines to be parallel is a = 4.
For which value of a are the graphs of –4 = 3x + 6y and ax – 8y = 12 parallel?
a = –4
a = -1/2
a = 1/4
a = 2
1 answer