Question

question
which equation represents a line which is parallel to the line $y = -\frac{5}{7}x - 7$?

answer
$\circ$ $5y - 7x = 20$ $\circ$ $5x + 7y = -42$
$\circ$ $5x - 7y = 56$ $\circ$ $7x + 5y = 10$

Explanation:

Step1: Recall parallel line slope rule

Parallel lines have equal slopes. The given line is \( y = -\frac{5}{7}x - 7 \), so its slope \( m = -\frac{5}{7} \). We need to find the slope of each option by converting to slope - intercept form \( y=mx + b \).

Step2: Analyze Option 1: \( 5y - 7x=20 \)

Solve for \( y \):
\( 5y=7x + 20 \)
\( y=\frac{7}{5}x + 4 \)
Slope \( m_1=\frac{7}{5}
eq-\frac{5}{7} \), so not parallel.

Step3: Analyze Option 2: \( 5x + 7y=-42 \)

Solve for \( y \):
\( 7y=-5x - 42 \)
\( y =-\frac{5}{7}x-6 \)
Slope \( m_2 =-\frac{5}{7} \), which is equal to the slope of the given line. Let's check other options for completeness.

Step4: Analyze Option 3: \( 5x - 7y = 56 \)

Solve for \( y \):
\( - 7y=-5x + 56 \)
\( y=\frac{5}{7}x - 8 \)
Slope \( m_3=\frac{5}{7}
eq-\frac{5}{7} \), so not parallel.

Step5: Analyze Option 4: \( 7x + 5y = 10 \)

Solve for \( y \):
\( 5y=-7x + 10 \)
\( y=-\frac{7}{5}x + 2 \)
Slope \( m_4 =-\frac{7}{5}
eq-\frac{5}{7} \), so not parallel.

Answer:

\( 5x + 7y=-42 \) (the second option among the given choices)