Chapter 4.2, Problem 64SR

To determine

To find: The equation in function notation for the graph of line passing through the points $\left(0,0\right)$ and $\left(2,1\right)$ as shown in graph.

  

Answer to Problem 64SR

The equation in function notation of straight line is $y=\frac{1}{2}x$ .

Explanation of Solution

Given information: From the given graph of the line, the line passes through the points $\left(0,0\right)$ and $\left(2,1\right)$ . Also, the line passes through the origin as given in graph, therefore y-intercept $c=0$ of the given line.

Calculation: The slope of the line passing through the points $\left(0,0\right)$ and $\left(2,1\right)$ is calculated as,

  $\begin{array}{c}m=\frac{1-0}{2-0}\left(\begin{array}{l}\text{Using formula for}\\ \text{slope}\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\end{array}\right)\\ =\frac{1}{2}\mathrm{......}\left(1\right)\end{array}$

Also, the line passes through the origin as given in graph, therefore y-intercept $c=0$ of the line. Therefore, using slope-intercept form $y=mx+c$ the equation of the line is evaluated as,

  $\begin{array}{l}y=\left(\frac{1}{2}\right)x+\left(0\right)\mathrm{......}\left(\begin{array}{l}\text{Plugging for }c=0\\ \text{and }m=\frac{1}{2}\text{ from }\left(1\right)\end{array}\right)\\ y=\frac{1}{2}x\end{array}$