Chapter 4, Problem 22SGR

To determine

To find:The equation of the line for the given condition.

Answer to Problem 22SGR

The equation of the straight line for the given condition is $y=-\frac{1}{3}x-\frac{1}{3}$ .

Explanation of Solution

Given:

The equation passes through point $\left(5,-2\right)$

The slope of the equation m = $-\frac{1}{3}$

Calculation:

The standard form of slope and point form of the straight line is $y-y_1=m\left(x-x_1\right)$ .

Here m is the slope of the straight line and $\left(x_1,y_1\right)$ is the point from which the straight line passes.

Substitute $-\frac{1}{3}$ for slope m and $\left(5,-2\right)$ for $\left(x_1,y_1\right)$ .

The equation of the straight line is

  $\begin{array}{l}y-\left(-2\right)=-\frac{1}{3}\left(x-\left(5\right)\right)\\ y=-\frac{1}{3}x+\frac{5}{3}-2\\ y=-\frac{1}{3}x-\frac{1}{3}\end{array}$

Therefore, the equation of the straight line is $y=-\frac{1}{3}x-\frac{1}{3}$ .