Chapter 8.5, Problem 2C

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 2C

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

Explanation of Solution

Given:

An equation: $3x-2y=6$ .

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:

  $\begin{array}{l}3x-2y=6\left(\text{Given equation}\right)\\ 3x-3x-2y=6-3x\left(\text{Subtracting }3x\text{from both sides}\right)\\ -2y=-3x+6\\ \frac{-2y}{-2}=\frac{-3x}{-2}+\frac{6}{-2}\left(\text{Dividing both sides by }-2\right)\\ y=\frac{3}{2}x-3\end{array}$

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

We will start from drawing the y- intercept of our given line. The y -intercept of our given line is $-3$ , so we will start our line from $(0,-3)$ .

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

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