Q. 83 - 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.

$x=-4$

Step-by-Step Solution

Answer

Slope is undefined

y-intercept is undefined

The graph is 

Verification:

Both graphs are the same.

Step 1. Given information

The equation of a line is 

$x=-4$

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

The equation of the line is 

$x=-4$

Since this line is parallel to y-axis and any line parallel to y-axis is always vertical line.

Slope of vertical line is always undefined.

So, slope of this line is undefined

and y-intercept of this line is also undefined.

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-value is always $-4$ for any values of y.

$x$	$y$
$-4$	$1$
$-4$	$2$
$-4$	$3$

Locate points $(-4,1),(-4,2),(-4,3)$on the graph and 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.