Question

Create an equation of a line that is perpendicular to the equation f (x) = 5x – 4

Answer 1

The given linear function is

`f(x)=5x-4`

This equation represents a straight line with a slope of 5. (Remember that the slope is the coefficient of the x).

Since we have to find a perpendicular line to f(x), we have to use the perpendicularity criteria to find the slope first:

`m_1\cdot m_2=-1`

Where the first slope is 5.

`\begin{gathered} 5\cdot m_2=-1 \\ m_2=-(1)/(5) \end{gathered}`

This means the new perpendicular line has a slope of -1/5.

Now, we use this slope, a random point (-1,2), and the point-slope formula, to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-(1)/(5)(x-(-1)) \\ y=-(1)/(5)(x+1)+2 \\ y=-(1)/(5)x-(1)/(5)+2 \\ y=-(1)/(5)x-(1+10)/(5) \\ y=-(1)/(5)x-(11)/(5) \end{gathered}`

Therefore, a perpendicular line to f(x) would be

`y=-(1)/(5)x-(11)/(5)`