Chapter 3.5, Problem 27E

To determine

To graph the linear equation:

$y=2x$

And identify the x -intercept.

Answer to Problem 27E

The x -intercept is at $x=0$ .

Explanation of Solution

Given:

$y=2x$

Concept Used:

To graph a linear equation $y=mx+c$ :

1. Note slope of equation and y -intercept, that are, m and $\left(0,c\right)$ respectively.
2. Use slope to find another point in line, as
$\text{slope}=\frac{\text{rise}}{\text{run}}$
3. Draw a line through the points in above step.
4. The point where the line that crosses the x -axis is x -intercept of graph of the equation.

Calculation:

In order to graph the linear function:

$y=2x$

First, note the slope of equation and y -intercept.

Comparing given equation with $y=mx+c$ , gives $m=2,\text{ and }c=0$

So slope and y- intercept of given equation are $2,\text{ and }\left(0,0\right)$ , respectively.

Now, find another point using slope:

$\begin{array}{c}\text{slope}=\frac{\text{rise}}{\text{run}}\\ =\frac{2}{1}\end{array}$

Since, rise is 2 and run is 1, so go up 2 unit down and 1 unit right from point $\left(0,0\right)$ . That is the new is: $\left(0+1,0+2\right)=\left(1,2\right)$

Now, finally to draw the graph of given linear equation plot these points, $\left(0,0\right)$ and $\left(1,2\right)$ using a graphing utility and draw a line through them. The graph is represented as:

Since, the graph(line) of the given equation crosses the x -axis at $\left(0,0\right)$ , so the x -intercept of graph of the equation is at $x=0$ .