Question

Which equation represents a line which is parallel to the line x + 8y = 56?

Answer 1

Explanation

when two lines are parallel, their slopes are equal

if two lines with slope(m1) and slope(2) are parallel,then

$m_{_1}=m_2$

Step 1

convert the function into the form

$\begin{gathered} y=\text{ mx+b } \\ \text{where m is the slope} \end{gathered}$

then,

$\begin{gathered} x+8y=56 \\ i)\text{ subtract x in both sides} \\ x+8y-x=56-x \\ 8y=56-x \\ divide\text{ both sides by 8} \\ \frac{8y}{8}=\frac{56}{8}-\frac{x}{8} \\ \\ y=-\frac{1}{8}x+7\rightarrow y=mx+b \end{gathered}$

so, the slope of the function we are looking for is -1/8

Step 2