Chapter 4, Problem 25MCQ

To determine

To write:The equation in the slope intercept form for the line that passes through the given point and is perpendicular to the given equation.

Answer to Problem 25MCQ

The equation in the slope intercept form for the line that passes through the given point and is perpendicular to the given equation is $y=2x-2$ .

Explanation of Solution

Given:

The equation is $-x-2y=0$ .

The line passes through the point $\left(-1,-4\right)$

Calculation:

Calculate the slope of the first equation. Convert the given equation in the standard slope and intercept form of the equation $y=mx+c$ , the slope of the first equation is:

  $\begin{array}{l}-x-2y=0\\ 2y=-x\\ y=\frac{-1}{2}x\\ \text{The slope of the equation is }\\ m=\frac{-1}{2}\end{array}$

Calculate the slope of the second line which is perpendicular to the given line.

  $\begin{array}{l}{m}_1{m}_2=-1\\ \left(\frac{-1}{2}\right)m_2=-1\\ m_2=2\end{array}$

Substituting the value of slope and point in the standard form of slope and point form of the equation.

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-4\right)=2\left(x-\left(-1\right)\right)\\ y+4=2x+2\\ y=2x-2\end{array}$

Therefore, the equation in the slope intercept form for the line that passes through the point $\left(-1,-4\right)$ and is perpendicular to the given equation is $y=2x-2$ .