Answer:
See Explanation
Step-by-step explanation:
Given
See attachment for graph
Required
A situation that can be modeled by the graph.
The prompt and the response are as follows:
The type of function:
It is a linear function
The variables modeled in the function
The variables are x and y
The domain and the range
From the graph, we can see that x and y values are not limited to any constraints.
So, the domain and the range are:
[tex]Domain: \{-\infty \le x \le \infty \}[/tex]
[tex]Range: \{-\infty \le y \le \infty \}[/tex]
Question that could be [tex]answered[/tex]
The graph could be used to predict y value, given the x value.
Take for instance, find y when x = 10
The answer can be handpicked directly from the graph. However, the best way is to calculate the graph equation, first.
So, we have:
Pick any two points on the line of the graph
[tex](x_1,y_1) = (-2,0)[/tex]
[tex](x_2,y_2) = (0,4)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4 - 0}{0 - -2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m =2[/tex]
The equation of the graph is:
[tex]y = m(x - x_1) + y_1\\[/tex]
So, we have:
[tex]y = 2(x - -2) + 0[/tex]
[tex]y = 2(x +2)[/tex]
Expand
[tex]y = 2x +4[/tex]
To solve for y when x = 10;
[tex]y = 2 * 10 +4[/tex]
[tex]y = 20 +4[/tex]
[tex]y = 24[/tex]
