Q. 71 - 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.

$y=2x+3$

Step-by-Step Solution

Answer

Slope is $2$

y-intercept is $(0,3)$

The graph is 

Verification:

Both graphs are the same.

Step 1. Given information

The equation of a line is 

$y=2x+3$

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

The equation of line is $y=2x+3$

Compare with slope-intercept formula of a line 

$y=mx+b$

So, $m=2,b=3$

Therefore, 

slope is $2$

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

$x$	$y=2x+3$
$-2$	$-1$
$0$	$3$
$2$	$7$

Locate points $(-2,-1),(0,3),(2,7)$ 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.