Chapter 8.6, Problem 9E

To determine

To plot: The points on the graph and identify the representation of the points.

Answer to Problem 9E

Thepoints represent thelinearequation.

Explanation of Solution

Given information:

The points are $\left(-2,-1\right),\left(-1,0\right),\left(1,2\right)\left(2,3\right),\left(0,1\right)$ .

Plot the points on the graph as shown in Figure 1.

  

The linear function is monotonic and straight line that is defined on the set of real numbers.

The equation of the linear function is $y=mx+b$ where the value of $m$ is the slope and $b$ is the $y$ -intercept.

It can be seen from the graph that the points are $\left(-2,-1\right),\left(-1,0\right),\left(1,2\right)\left(2,3\right),\left(0,1\right)$ .

If the slope from any points on the graph provide same slope then then the given equation is the linear equation.

Find the slope of the line from the provided points $\left(-2,-1\right),\left(-1,0\right)$ .

  $\begin{array}{c}m=\frac{0-\left(-1\right)}{-1-\left(-2\right)}\\ =1\end{array}$

Find the slope of the line from the provided points $\left(2,3\right),\left(0,1\right)$ .

  $\begin{array}{c}m=\frac{1-3}{0-2}\\ =1\end{array}$

It can be seen the slope of from any point on the graph is same that means the points on the graph represents the line.

Therefore, the points on the graph represents the equation of linear function.