Chapter 4.3, Problem 49PFA

To determine

To Find: The equation of the line represented by the graph

Answer to Problem 49PFA

The equation of line represent the new street is $y=\frac{1}{2}x+2$ option ‘B’ is correct.

Explanation of Solution

Given information:

The graph

Concept and Formula Used:

Equation of line passing through two points is given by $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$ . Slope intercept form $y=mx+c$

Calculation:

The graph of the line given by

From the graph line passes from two points i.e. $\left(0,2\right)\&\left(-4,0\right)$

Equation of line through two points is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(0,2\right)\&\left(x_2,y_2\right)=\left(-4,0\right)\\ y-\left(2\right)=\left(\frac{0-\left(2\right)}{-4-\left(0\right)}\right)\left(x-0\right)\\ y-2=\left(\frac{-2}{-4}\right)\left(x\right)\\ y-2=\frac{1}{2}x\\ \text{Add 2 on both sides}\\ y-2+2=\frac{1}{2}x+2\\ y=\frac{1}{2}x+2\end{array}$

Conclusion:

The equation of line represent the new street is $y=\frac{1}{2}x+2$ option ‘B’ is correct.