Question

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

$3x+2y=6$

Short answer

Slope is$-\frac{3}{2}$

y-intercept is$(0,3)$

The graph is

Verification:

Both graphs are the same.

Step-by-step solution

Step 1. Given information

The equation of a line is

$3x+2y=6$

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

The equation of the line is

$3x+2y=6$

Solve for $y$

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

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

So,

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

Therefore,

slope is $-\frac{3}{2}$

y-intercept is$(0,3)$

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

$x$	$y$
$-2$	$6$
$0$	$3$
$2$	$0$

Locate points$(-2,6),(0,3),(2,0)$ 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.