Chapter 4.2, Problem 16PPS

To determine

To find: The equation of the line.

Answer to Problem 16PPS

The equation of the line is $x+y=7$

Explanation of Solution

Given:

The points are $\left(9,-2\right)\text{ and }\left(4,3\right)$ 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,

  $x_1=9,y_1=-2,x_2=4,y_2=3$

The slope can be computed as:

  $\begin{array}{c}b=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{3-\left(-2\right)}{4-9}\\ =\frac{5}{-5}\\ =-1\end{array}$

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

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-2\right)=-1\left(x-9\right)\\ y+2=-x+9\\ x+y=7\end{array}$

Hence, the required equation of the line is $x+y=7$ .