Chapter 1, Problem 42SGA

To determine

To find: the slope-intercept form of line equation.

Answer to Problem 42SGA

  $y=\frac{1}{2}x+4$

Explanation of Solution

Given information:

  $\begin{array}{c}\left(x_1,y_1\right)=\left(-4,2\right)\\ \left(x_2,y_2\right)=\left(2,5\right)\end{array}$

Calculation:

Substitute the values into the slope formula to evaluate slope as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{5-2}{2-\left(-4\right)}\\ =\frac{3}{2+4}\\ =\frac{3}{6}\\ =\frac{1}{2}\end{array}$

The slope intercept form of equation is as follows:

  $y=mx+b$

Substitute the values of slope (m) and one of the coordinates $\left(2,5\right)$ in the above equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ 5=\left(\frac{1}{2}\right)\left(2\right)+b\\ 5=1+b\\ b=5-1\\ =4\end{array}$

Now put the value of m and b in the slope intercept form as shown below.

  $\begin{array}{l}y=mx+b\\ y=\frac{1}{2}x+4\end{array}$

Thus, the slope intercept form of line is $y=\frac{1}{2}x+4$ .