Question

For what value of k are the graphs of 12y = 9x + 8 and 4y = k(x + 4) parallel?

perpendicular? I HAVE THE ANSWER, just need step to step explanation on how to solve it (pls be clear, answers in pic)

Answer 1

• parallel: k = 3
• perpendicular: k = -16/3

Explanation:

You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.

Parallel

The slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...

• y = k/4x +1
• y = 3/4x +2/3

For parallel lines, we want to choose the value of k so that the slopes are equal:

k/4 = 3/4

k = 3 . . . . . . . . multiply by 4

Perpendicular

The slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...

(k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1

k = -16/3 . . . . . . . . . multiply by 16/3

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Additional comment

The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.