Chapter 8.8, Problem 50STP

To determine

To calculate: To find the equation that best describes the line graphed.

Answer to Problem 50STP

Theequation of line is $y=\frac{1}{4}x-2$

Explanation of Solution

Given information: Graph of line is

  

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Calculation:

Graph of line is given as follows:

  

From the graph, the line crosses y-axis at point $\left(0,-2\right)$

Thus, y-intercept is given as

  $c=-2$

Also, When $x=4$ ,

  $y=-1$

Thus, slope is calculated as

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values, slope is

  $\begin{array}{l}m=\frac{-1-\left(-2\right)}{4-0}\\ m=\frac{-1+2}{4}\\ m=\frac{1}{4}\end{array}$

Using slope intercept form of line, equation of line is given as

  $y=mx+c$

Substituting the values in above equation,

  $\begin{array}{l}y=\frac{1}{4}x+\left(-2\right)\\ y=\frac{1}{4}x-2\end{array}$

Conclusion:

Hence, the equation of line is $y=\frac{1}{4}x-2$

Correct option is B.