Question

Which equation represents a line which is perpendicular to the line 8x + 3y = 32?

Answer 1

Let's re-arrange the equation in slope-intercept form, which is y = mx + b.

`\begin{gathered} 8x+3y=32 \\ 3y=-8x+32 \\ y=(-8x+32)/(3) \\ y=-(8)/(3)x+(32)/(3) \end{gathered}`

The line that is perpendicular will have a slope that is negative reciprocal of the slope of this line.

The slope of this line is -8/3.

Hence, the negative reciprocal of -8/3 is 3/8.

The choices are:

`\begin{gathered} y=(3)/(8)x-4 \\ \text{and} \\ y=-(3)/(8)x-7 \end{gathered}`

The first one is the line perpendicular since its slope is 3/8.

Answer
`y=(3)/(8)x-4`