Q. 79 - Precalculus Enhanced with Graphing Utilities

Question

Find the slope and y-intercept of each line. Graph the line by hand. Verify using a graphing utility.

$2x-3y=6$

Step-by-Step Solution

Answer

Slope is $\frac{2}{3}$

y-intercept is $(0,-2)$

The graph is 

Verification:

Both graphs are the same.

Step 1. Given information

The equation of a line is 

$2x-3y=6$

Step 2. Finding the slope of line and y-intercept

The equation of the line is 

$2x-3y=6$

Solve for $y$

$$\begin{gathered} 2x-3y-2x=6-2x \\ -3y=-2x+6 \\ \frac{-3y}{-3}=\frac{-2x}{-3}+\frac{6}{-3} \\ y=\frac{2}{3}x-2 \end{gathered}$$

Compare with slope-intercept formula of a line $y=mx+b$

So, 

$$\begin{gathered} m=\frac{2}{3} \\ b=-2 \end{gathered}$$

Therefore, 

Slope is $\frac{2}{3}$

y-intercept $(0,-2)$

Step 3. Graphing the line by hand

Firstly, we can make a table of x and y values by selecting some random values of x and find y

$x$	$y$
$-3$	$-4$
$0$	$-2$
$3$	$0$

Locate points $(-3,-4),(0,-2),(3,0)$ on the graph and then join them to sketch the graph 

Step 4. Verify graph using the graphing utility

The graph  by hand is 

The graph using calculator is 

Here,  both graphs are the same.