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=(-8x)/(3)-(12)/(3) \\ y=(-8x)/(3)-4 \\ \text{Here, slope is }(-8)/(3) \\ (-8)/(3)\\e(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=(8)/(3)x-(18)/(3) \\ y=(8)/(3)x-6 \\ \text{Slope is }(8)/(3) \\ \text{Thus, }(8)/(3)\\e(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=(3)/(8)x+(32)/(8) \\ y=(3)/(8)x+4 \\ \text{Slope is }(3)/(8) \\ (3)/(8)=(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=(8)/(8)-(3)/(8)x \\ y=1-(3)/(8)x \\ \text{Slope is }-(3)/(8) \\ (-3)/(8)\\e(3)/(8) \\ \text{The equation of line is not parallel to the given equation of line.} \end{gathered}`

Answer : C) 8y - 3x = 32