Question

Graphing Linear Functions For the given linear function, make a table of values and sketch its graph. What is the slope of the graph?

$g\left(x\right)=4-2x$

Short answer

The graph of the given function is shown below and the slope of the graph is $-2$.

Step-by-step solution

Step 1. Linear function.

A linear function can be written as:

$f\left(x\right)=ax+b$

Where$a$ is the rate of change (slope) and$b$ is the initial value ($y$-intercept), and both are real numbers.

Step 2. Given function and table of values.

The given function is:

$g\left(x\right)=4-2x$

Table of values for the given function is:

$x$	$g\left(x\right)$
-2	8
-1	6
0	4
1	2
2	0

Step 3. Graph of the linear function.

Plot the points on a coordinate plane from the above table of values and connect them by a straight line as shown below.

Step 4. Find the slope.

The given function can be written as:

$g\left(x\right)=4-2x$

It can be rewritten as:

$g\left(x\right)=-2x+4$

Comparing$g\left(x\right)=-2x+4$and$f\left(x\right)=ax+b$to find the slope.

$a=-2$

Thus, the graph of the given function is in step$3$and the slope of the graph is $-2$.