Problem
X (with MTH 104) - Summer 2023 - Avery
Navayha Smith $\quad 06 / 12 / 23$ 6:09 PM
15.3 - Writing
HW Score: $61.9 \%, 13$ of Lines
21 points
Points: 0 of 1
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Determine whether the following pair of lines are parallel, perpendicular, or neither.
\[
\begin{array}{l}
5 x=4 y+1 \\
-10 x+8 y=1
\end{array}
\]
Choose the correct answer below.
A. Perpendicular
B. Neither
C. Parallel
Solution
Step 1 ：Rewrite the given equations in slope-intercept form (y = mx + b):
Step 2 ：\(y = \frac{5}{4}x - \frac{1}{4}\) for the first equation
Step 3 ：\(y = \frac{5}{4}x + \frac{1}{8}\) for the second equation
Step 4 ：Compare the slopes of both equations:
Step 5 ：\(m_1 = \frac{5}{4}\) and \(m_2 = \frac{5}{4}\)
Step 6 ：Since the slopes of both lines are equal, the lines are parallel.
Step 7 ：\(\boxed{\text{C. Parallel}}\)
