Question

Consider the graph above. Write about a situation that could be modeled using this graph. In your response, use the prompts below to guide your thinking:

Answer 1

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:

$Domain: \{-\infty \le x \le \infty \}$

$Range: \{-\infty \le y \le \infty \}$

Question that could be $answered$

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

$(x_1,y_1) = (-2,0)$

$(x_2,y_2) = (0,4)$

Calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - 0}{0 - -2}$

$m = \frac{4}{2}$

$m =2$

The equation of the graph is:

$y = m(x - x_1) + y_1$

So, we have:

$y = 2(x - -2) + 0$

$y = 2(x +2)$

Expand

$y = 2x +4$

To solve for y when x = 10;

$y = 2 * 10 +4$

$y = 20 +4$

$y = 24$