Question

which equation represents a line which is parallel to the line $y = \frac{8}{5}x - 5$?

answer

$\circ$ $5x + 8y = -32$ $\circ$ $8x + 5y = 35$
$\circ$ $8y - 5x = -48$ $\circ$ $8x - 5y = -10$

Explanation:

Step1: Identify slope of given line

Given line \( y = \frac{8}{5}x - 5 \) has slope \( m = \frac{8}{5} \).

Step2: Convert options to slope-intercept form

Option1: \( 5x + 8y = -32 \)

\( 8y = -5x -32 \) → \( y = -\frac{5}{8}x -4 \), slope \( -\frac{5}{8} \) (not parallel)

Option2: \( 8x + 5y = 35 \)

\( 5y = -8x +35 \) → \( y = -\frac{8}{5}x +7 \), slope \( -\frac{8}{5} \) (not parallel)

Option3: \( 8y -5x = -48 \)

\( 8y = 5x -48 \) → \( y = \frac{5}{8}x -6 \), slope \( \frac{5}{8} \) (not parallel)

Option4: \( 8x -5y = -10 \)

\( -5y = -8x -10 \) → \( y = \frac{8}{5}x +2 \), slope \( \frac{8}{5} \) (parallel)
Wait correction: Option3 was miscalculated. Recheck option3: \(8y -5x=-48\) → \(8y=5x-48\) → \(y=(5/8)x-6\) (slope 5/8). Option4: \(8x-5y=-10\) → \(5y=8x+10\) → \(y=(8/5)x+2\) (slope 8/5, same as given line). So correct option is 8x -5y=-10? Wait no: original given slope is 8/5. So option4 slope is 8/5, yes. So answer is 8x -5y=-10? Wait no wait: 8x -5y=-10 → -5y = -8x -10 → y=(8/5)x +2, yes slope 8/5. So correct answer is 8x -5y=-10? Wait but let's recheck:

Wait the options are:

1.5x+8y=-32 → slope -5/8

2.8x+5y=35 → slope -8/5

3.8y-5x=-48 → slope 5/8

4.8x-5y=-10 → slope 8/5

Yes, so option4 has same slope as given line, so it's parallel. So answer is 8x -5y = -10.

Step1: Find slope of given line

Given line \( y = \frac{8}{5}x -5 \) has slope \( \frac{8}{5} \).

Step2: Calculate slopes of options

• \(5x+8y=-32\): \(y=-\frac{5}{8}x-4\), slope \( -\frac{5}{8} \)
• \(8x+5y=35\): \(y=-\frac{8}{5}x+7\), slope \( -\frac{8}{5} \)
• \(8y-5x=-48\): \(y=\frac{5}{8}x-6\), slope \( \frac{5}{8} \)
• \(8x-5y=-10\): \(y=\frac{8}{5}x+2\), slope \( \frac{8}{5} \)

Step3: Select parallel line

Only \(8x-5y=-10\) has same slope as given line.

Answer:

8y - 5x = -48