Chapter 11.1, Problem 6QR

Solution

To find: The equation of the line using the given slope and the points.

The equation of the line is given by $y-4=\frac{-4}{3}\left(x-1\right)$ .

Given data:

The line is passing through the point $\left(1,4\right)$ and perpendicular to the line $y=\frac{3}{4}x+2$ .

Formula used:

If $m_1$ and $m_2$ are the slopes of lines that are perpendicular to each other.

  $m_1\times m_2=-1$

Let $\left(x_1,y_1\right)$ and $m$ are the point on a line and slope of the line respectively, then the equation of line in point slope form is determined by:

  $y-y_1=m\left(x-x_1\right)$

Calculation:

It is given that the line is perpendicular to the line $y=\frac{3}{4}x+2$ whose slope is $\frac{3}{4}$ . Let the slope of line be $m$ .

  $\begin{array}{c}m\times \frac{3}{4}=-1\\ m=\frac{-4}{3}\end{array}$

Compute the equation of line which is passing through $\left(1,4\right)$ and has slope $\frac{-4}{3}$ .

  $y-4=\frac{-4}{3}\left(x-1\right)$

Therefore, the equation of the line is given by $y-4=\frac{-4}{3}\left(x-1\right)$ .