Chapter 1, Problem 41SGA

To determine

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

Answer to Problem 41SGA

  $y=\frac{1}{2}x+\frac{9}{2}$

Explanation of Solution

Given information:

  $\begin{array}{c}\left(x,y\right)=\left(-5,2\right)\\ m=\frac{1}{2}\end{array}$

Calculation:

The slope intercept form of equation is as follows:

  $y=mx+b$

Substitute the values of slope (m) and point of coordinates in the above equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ 2=\left(\frac{1}{2}\right)\left(-5\right)+b\\ 2=\frac{-5}{2}+b\\ b=2+\frac{5}{2}\\ =\frac{4+5}{2}\\ =\frac{9}{2}\end{array}$

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

  $y=\frac{1}{2}x+\frac{9}{2}$

Thus, the slope intercept form of line is $y=\frac{1}{2}x+\frac{9}{2}$ .