Chapter 9, Problem 23CCSR

To determine

To determine the equation of the line.

Answer to Problem 23CCSR

The equation is $y=\left(-\frac{1}{4}\right)x+1$

Explanation of Solution

Given information:

Equation of line $p$ is $y=4x-3$

Equation of the line is in the form $y=mx+c$ where $m$ is slope of the line and $c$ is any constant.

Given that the line $n$ is perpendicular to the line $y=4x-3$ .

Now we know that if two lines are perpendicular, then multiplication of their slopes will give -1.

Slope of line $p$ is 4.

Hence we get,

  $\begin{array}{l}{m}_n\times 4=-1\\ m_n=-\frac{1}{4}\end{array}$

Slope of line $n=-\frac{1}{4}$

Now it is given that the point (8, -1) is on the line.

Now we shall determine the equation of the line.

  $y=\left(-\frac{1}{4}\right)x+c$

Put values of the points we get,

  $\begin{array}{l}-1=\left(-\frac{1}{4}\right)8+c\\ c=-1+2=1\end{array}$

Hence the equation is $y=\left(-\frac{1}{4}\right)x+1$