Chapter 4.1, Problem 17PPS

To determine

To find: The equation of the line.

Answer to Problem 17PPS

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

Explanation of Solution

Given:

The points are $\left(-2,5\right)\text{ and }\left(5,-2\right)$ 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,

  $x_1=-2,y_1=5,x_2=5,y_2=-2$

The slope can be computed as:

  $\begin{array}{c}b=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{\left(-2\right)-5}{5-\left(-2\right)}\\ =\frac{-7}{7}\\ =-1\end{array}$

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

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-5=-1\left(x-\left(-2\right)\right)\\ y-5=-x-2\\ x+y=3\end{array}$

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