h MTH 104) - Summer 2023 - Avery
Navayha Smith $06 / 12 / 23$ 6:08 PM
- Writing
Question 13, 18.6.2
HW Score: $61.9 \%, 13$ of
Part 1 of 2
21 points
Points: 0 of 1
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Find the slope of a line parallel and perpendicular to the given line.
\[
4 x+12 y=36
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope of a line parallel to the given line is
(Simplify your answer.)
B. The slope is undefined.

Step 1 ：Rewrite the given equation in slope-intercept form (y = mx + b): \(4x + 12y = 36\) becomes \(y = -\frac{1}{3}x + 3\)

Step 2 ：Identify the slope of the given line as \(-\frac{1}{3}\)

Step 3 ：Since parallel lines have the same slope, the slope of a line parallel to the given line is also \(-\frac{1}{3}\)

Step 4 ：Find the slope of a line perpendicular to the given line by taking the negative reciprocal of the given line's slope: \(\frac{-1}{-\frac{1}{3}} = 3\)

Step 5 ：\(\boxed{\text{The slope of a line parallel to the given line is } -\frac{1}{3} \text{, and the slope of a line perpendicular to the given line is } 3}\)