Question

Write an equation of a line that is perpendicular to y=(1/4)x+5 and contains the point (2,-3).

Answer 1

Step-by-step explanation:

Let's say that we have the line y=(1/4)x + 5 and the perpendicular line y' = mx+c.

The slope of the line (m) y' can be calculated as follows:

`m_(y^(\prime)).m_y=-1`

So,

`\begin{gathered} m_(y^(\prime)).(1)/(4)=-1 \\ m_(y^(\prime))=-1\cdot(4)/(1) \\ m_(y^(\prime))=-4 \end{gathered}`

We can write the line y' as y'= -4x + b.

Now, we can use the point (2, -3) to find the value of b:

`\begin{gathered} y^(\prime)=-4x+b \\ -3=-4(2)+b \\ -3=-8+b \\ -3+8=b \\ b=5 \end{gathered}`