Chapter 6.6, Problem 77E

To determine

To calculate: .The equation in point slope form.

Answer to Problem 77E

The required equation is $y=-\frac{1}{3}x-7$ .

Explanation of Solution

Given Information:

The given point is $\left(3,-8\right)$ and slope of a line $m=-\frac{1}{3}$ .

Formula Used:

Point slope form:

  $y-y_1=m\left(x-x_1\right)$

Calculation:

Consider the point is $\left(3,-8\right)$ .

Now, find an equation in point slope form; use point slope form.

  $y-y_1=m\left(x-x_1\right)$

Substitute $3$ for $x_1$ , $-8$ for $y_1$ and $-\frac{1}{3}$ for $m$ in the above equation.

  $y-\left(-8\right)=\left(-\frac{1}{3}\right)\left(x-3\right)$

Simplify the above equation.

  $\begin{array}{c}y-\left(-8\right)=\left(-\frac{1}{3}\right)\left(x-3\right)\\ y+8=-\frac{1}{3}x+1\\ y=-\frac{1}{3}x+1-8\\ y=-\frac{1}{3}x-7\end{array}$

Hence, the required equation is $y=-\frac{1}{3}x-7$ .