Question

select all the equations that represent lines that are parallel to the graph of 8x + 2y = 7.
a ( y - 1 = 4(x + 8) )
b ( y = -4x + 15 )
c ( 16x + 4y = 9 )
d ( y = -4x )
e ( 4x + 2y = 3 )

Explanation:

Step1: Find slope of \(8x + 2y = 7\)

Rewrite in slope - intercept form \(y=mx + b\) (where \(m\) is slope).
\(2y=-8x + 7\)
\(y=-4x+\frac{7}{2}\). So slope \(m=-4\).

Step2: Analyze Option A

\(y - 1 = 4(x + 8)\)
\(y-1 = 4x+32\)
\(y = 4x+33\). Slope \(m = 4
eq - 4\). Not parallel.

Step3: Analyze Option B

\(y=-4x + 15\). Slope \(m=-4\). Parallel (same slope).

Step4: Analyze Option C

\(16x + 4y = 9\)
\(4y=-16x + 9\)
\(y=-4x+\frac{9}{4}\). Slope \(m=-4\). Parallel.

Step5: Analyze Option D

\(y=-4x\). Slope \(m=-4\). Parallel.

Step6: Analyze Option E

\(4x + 2y = 3\)
\(2y=-4x + 3\)
\(y=-2x+\frac{3}{2}\). Slope \(m=-2
eq - 4\). Not parallel.

Answer:

B. \(y = - 4x+15\), C. \(16x + 4y = 9\), D. \(y=-4x\)