Chapter 4.2, Problem 33PPS

To determine

The equation in standard form for line with coordinates (-1, 7) and (8, -2).

Answer to Problem 33PPS

The standard equation of line is $x+y=6$ .

Explanation of Solution

Given:

The line has coordinates (-1, 7) and (8, -2).

Calculation:

Slope of the line is calculated as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-2-7}{8-\left(-1\right)}\\ =-1\end{array}$

Point slope form of line is expressed as follows:

  $y-y_1=m\left(x-x_1\right)$

Here, m is slope.

Substitute the slope and coordinate in the point slope form as follows:

  $\begin{array}{l}y-7=-1\left(x-\left(-1\right)\right)\\ y-7=-\left(x+1\right)\end{array}$

Standard form is calculated as follows:

  $\begin{array}{l}y-7=-\left(x+1\right)\\ y-7=-x-1\\ x+y=6\end{array}$

Thus, the standard equation of line is $x+y=6$ .