Q. 72 - 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.

$y=-3x+4$

Step-by-Step Solution

Answer

Slope is $-3$

y-intercept is $(0,4)$

The graph is 

Verification:

Both graphs are the same.

Step 1. Given information

The equation of a line is 

$y=-3x+4$

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

The equation of line is $y=-3x+4$

Compare with slope-intercept formula of a line 

$y=mx+b$

So,

 $$\begin{gathered} m=-3 \\ b=4 \end{gathered}$$

Therefore,

slope is $-3$

y-intercept is $(0,4)$

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

$x$	$y=-3x+4$
$-1$	$7$
$0$	$4$
$1$	$1$

Locate points $(-1,7),(0,4),(1,1)$on the graph and join them to get the equation of line.

Step 4. Verify graph using the graphing utility

The graph by hand is

The graph using a calculator is

Here,  both graphs are the same.