Chapter 8.6, Problem 45E

To determine

To find: the standard form of equation of line.

Answer to Problem 45E

  $x-y+4=0$

Explanation of Solution

Given information:

The equation of graph which is parallel to the line and the points that lie on the line is shown below.

  $\begin{array}{l}y=x-8\\ \left(-3,1\right)\end{array}$

Calculation:

The slope of two parallel lines is equal. So first compare the given equation with slope intercept equation to find the value of slope as shown below.

  $\begin{array}{l}y=mx+b\\ y=x-8\\ \therefore m=1\end{array}$

Thus the slope is 1.

Now put the point coordinates and the value of slope in the equation given below to evaluate the standard form of equation.

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ y-1=1\left(x-\left(-3\right)\right)\\ y-1=x+3\\ y=x+3+1\\ y=x+4\\ 0=x-y+4\\ or\\ x-y+4=0\end{array}$

Thus the standard form of line is $x-y+4=0$ .