Chapter 4.2, Problem 2BCYP

To determine

To find: The equation of the line.

Answer to Problem 2BCYP

The equation of the line is $2x+3y=-14$

Explanation of Solution

Given:

The points are $\left(5,-8\right)\text{ and }\left(-7,0\right)$ respectively.

Concept used:

The equation of the line is:

  $\begin{array}{l}y=mx+b\\ \text{Where,}\\ m\text{ is the slope}\\ \text{a is the y-intercept}\end{array}$

The formula to compute the slope of the line is:

  $b=\frac{y_2-y_1}{x_2-x_1}$

Following point-slope formula is used to compute the equation of a line:

  $y-y_1=m\left(x-x_1\right)$

Calculation:

Here,

  $x_1=5,y_1=-7,x_2=0,y_2=-8$

The slope can be computed as:

  $\begin{array}{c}b=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{0-\left(-8\right)}{-7-5}\\ =\frac{8}{-12}\\ =-\frac{2}{3}\end{array}$

Now, the equation of line using the provided information can be calculated as:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-8\right)=-\frac{2}{3}\left(x-\left(5\right)\right)\\ y+8=\frac{-2x+10}{3}\\ 2x+3y=-14\end{array}$

Hence, the required equation of the line is $3x+y=9$ .