Question

Which equation represents a line which is perpendicular to the line x-5y=-40?A. y=5x+4B. y= 1/5x−1C. y=−5x−8D. y=− 1/5 x−7

Answer 1

In order to find the perpendicular line, we need to know that perpendicular lines have the following relation about their slopes:

`m_2=-(1)/(m_1)`

So first, let's find the slope of the given equation, putting it in the slope-intercept form (y = mx + b, m is the slope):

`\begin{gathered} x-5y=-40 \\ -5y=-x-40 \\ 5y=x+40 \\ y=(1)/(5)x+8 \end{gathered}`

The slope is m1 = 1/5. So the slope of any perpendicular line is:

`m_2=-(1)/((1)/(5))=-5`

So the perpendicular line has the model y = -5x + b

Therefore the correct option is C.