Chapter B, Problem 12E

To determine

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

Answer to Problem 12E

The equation of the line is $y=-\frac{7}{2}x-\frac{31}{2}$.

Explanation of Solution

Given:

The required line is passing through the point $\left(-3,-5\right)$ and the slope of the line is $-\frac{7}{2}$.

Property used:

The equation of the line passes through the point $\left(x_1,y_1\right)$ and having slope m is, $y-y_1=m\left(x-x_1\right)$.

Calculation:

Consider the given point be $\left(x_1,y_1\right)=\left(-3,-5\right)$ and the slope m = $-\frac{7}{2}$.

Substitute the values in the property mentioned above.

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-5\right)=\left(-\frac{7}{2}\right)\left(x-\left(-3\right)\right)\\ y+5=-\frac{7}{2}\left(x+3\right)\\ 2\left(y+5\right)=-7\left(x+3\right)\\ 2y+10=-7x-21\\ 2y=-7x-21-10\\ 2y=-7x-31\\ y=-\frac{7}{2}x-\frac{31}{2}\end{array}$

Thus, the equation of the line is $y=-\frac{7}{2}x-\frac{31}{2}$.