Question

Which equation represents a line which is parallel to the line y = 3/8x + 7?

Answer 1

The given equation of line is : y = 3/8x + 7

If two lines are parallel then the slopes of thier lines are equal.

The general equation of line is : y = mx + b, with slope is m :

Option : A)

$\begin{gathered} 8x+3y=-12 \\ 3y=-8x-12 \\ y=\frac{-8x}{3}-\frac{12}{3} \\ y=\frac{-8x}{3}-4 \\ \text{Here, slope is }\frac{-8}{3} \\ \frac{-8}{3}\ne\frac{3}{8} \\ Thus,\text{ the given equation of line is not parallel.} \end{gathered}$

Option : B)

$\begin{gathered} 8x-3y=18 \\ 3y=8x-18 \\ y=\frac{8}{3}x-\frac{18}{3} \\ y=\frac{8}{3}x-6 \\ \text{Slope is }\frac{8}{3} \\ \text{Thus, }\frac{8}{3}\ne\frac{3}{8} \\ \text{Thus the equation of line is not parallel to the given line} \end{gathered}$

Option C) :

$\begin{gathered} 8y-3x=32 \\ 8y=3x+32 \\ y=\frac{3}{8}x+\frac{32}{8} \\ y=\frac{3}{8}x+4 \\ \text{Slope is }\frac{3}{8} \\ \frac{3}{8}=\frac{3}{8} \\ \text{ Thus, the equation of line is parallel to the given equation of line} \end{gathered}$

The equation 8y - 3x = 32 is parallel to the line y = 3/8x + 7

Option D) :

$\begin{gathered} 3x+8y=8 \\ 8y=8-3x \\ y=\frac{8}{8}-\frac{3}{8}x \\ y=1-\frac{3}{8}x \\ \text{Slope is }-\frac{3}{8} \\ \frac{-3}{8}\ne\frac{3}{8} \\ \text{The equation of line is not parallel to the given equation of line.} \end{gathered}$

Answer : C) 8y - 3x = 32