Question

Two linear functions are created. The first linear function is represented by thegraph. The second linear function has the equation y = 2x+ 7. Describe the differencebetween the y-values of the two functions at x = 4?

Answer 1

State the given functions

The graph represented the first function and the second function is given as y = 2x+7

Find the value of y when x = 4 in the first function

From the graph, we can locate x = 4, and find the corresponding value of y.

To achieve this, from x = 4, trace to the line, and trace to the y-axis.

It can be observed from the graph that when x = 4, y = 4

Find the value of y when x = 4 in the second function

From the second function, we can find the value of y when x = 4.

To achieve this, put x = 4 in the equation to find the value of y as shown below:

`\begin{gathered} y=2x+7 \\ x=4 \\ y=2(4)+7 \\ y=8+7 \\ y=15 \end{gathered}`

Find the difference between the values of y when x =4 in the two functions

When x = 4, the value of y from the given graph is 4, and the value of y in the given equation of the second is 15

The difference is

`15-4=11`

Hence, the difference between the y-values of the two functions at x = 4 is 11