Question

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

$r\left(t\right)=-\frac{2}{3}t+2$

Short answer

The graph of the given function is shown below and the slope of the graph is $-\frac{2}{3}$.

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:

$r\left(t\right)=-\frac{2}{3}t+2$

Table of values for the given function is:

t	$r\left(t\right)$
-6	6
-3	4
0	2
3	0
6	-2

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:

$r\left(t\right)=-\frac{2}{3}t+2$

Comparing$r\left(t\right)=-\frac{2}{3}t+2$ and$f\left(x\right)=ax+b$ to find the slope.

$a=-\frac{2}{3}$

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