Chapter 3.4, Problem 4GP

To determine

To find:the equation of the line in slope intercept form the given graph.

Answer to Problem 4GP

The equation of the line $y=\frac{1}{4}x-1$

Option $A$ is correct

Explanation of Solution

Given information:

Consider

Formula used:

Slope intercept form of line is $y=mx+c$

Where m is the slope and c is the y- intercept.

Calculation:

From the graph, the line is passing through $(0,-1)\text{ and }(4,0)$

The slope of the line is

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{0+1}{4-0}=\frac{1}{4}\end{array}$

Then,

  $\begin{array}{l}y=mx+c\\ y=\frac{1}{4}x+c\\ (0,-1)\Rightarrow -1=0+c\\ c=-1\end{array}$

Hence,

The equation of the line $y=\frac{1}{4}x-1$

Option $A$ is correct