Chapter 6.7, Problem 66SR

To determine

To write: The slope intercepts form for the line

Answer to Problem 66SR

The slope intercept form of the line is $y=-\frac{1}{3}x-\frac{13}{3}$

Explanation of Solution

Given:

Equation: $y=-\frac{1}{3}x+3$

Point: $(-4,-3)$

Calculation:

If the equation of the line is $y=mx+c$ then slope of the line is $m$

Required line is parallel to the line with equation $y=-\frac{1}{3}x+3$

Since slope of parallel line is same, thus slope of the required line is $-\frac{1}{3}$

Required line passes through the point $(-4,-3)$ and has slope $-\frac{1}{3}$

Therefore the equation of the line is given by

  $\begin{array}{l}\frac{y-(-3)}{x-(-4)}=-\frac{1}{3}\\ 3(y+3)=-1(x+4)\\ 3y+9=-x-4\\ 3y=-x-13\\ y=-\frac{1}{3}x-\frac{13}{3}\end{array}$

Conclusion:

Hence, the slope intercept form of the line is $y=-\frac{1}{3}x-\frac{13}{3}$