Chapter 8.5, Problem 18E

To determine

To identify:

The slope and y -intercept of the line with the given equation. Use the slope and y -intercept to graph the equation.

Answer to Problem 18E

The slope of the lineis $\frac{2}{3}$ and the y -intercept is $0$ .

Explanation of Solution

Given:

An equation: $2x-3y=0$ .

Concept used:

The slope-intercept form of equation is $y=mx+b$ , where m represents slope of line and b represents the y -intercept.

Calculation:

First of all, we will convert our given equation in slope-intercept form as shown below:

  $\begin{array}{l}2x-3y=0\left(\text{Given equation}\right)\\ 2x-2x-3y=0-2x\left(\text{Subtracting }2x\text{from both sides}\right)\\ -3y=-2x\\ \frac{-3y}{-3}=\frac{-2x}{-3}\\ y=\frac{2}{3}x\end{array}$

Upon looking at our equation, we can see that the value of m is $\frac{2}{3}$ and the value of b is $0$ . Therefore, the slope of the line is $\frac{2}{3}$ and the y -intercept is $0$ .

We will start from drawing the y- intercept of our given line. The y -intercept of our given line is $0$ , so we will start our line from $(0,0)$ .

Since slope of our given line is $\frac{2}{3}$ , so rise is 2 and run is3.

Upon graphing our given equation, we will get our required graph as shown below: