To determine the rate of change of the function represented in the table and compare it with the function [tex]\( y = x + 4 \)[/tex], we need to follow these steps:
1. Identify Two Points in the Table:
Using the points [tex]\((0,6)\)[/tex] and [tex]\((2,8)\)[/tex] from the table.
2. Calculate the Rate of Change for the Table Function:
The rate of change (also known as the slope or [tex]\(m\)[/tex]) between any two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's apply this to our chosen points [tex]\((0,6)\)[/tex] and [tex]\((2,8)\)[/tex]:
[tex]\[
m = \frac{8 - 6}{2 - 0} = \frac{2}{2} = 1
\][/tex]
Thus, the rate of change of the function represented in the table is 1.
3. Compare with the Provided Function [tex]\( y = x + 4 \)[/tex]:
The function [tex]\( y = x + 4 \)[/tex] is a linear function in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope (rate of change). In this case, the slope [tex]\( m \)[/tex] is 1.
Now, we can complete the given statement:
"The rate of change in the function [tex]\( y = x + 4 \)[/tex] is equal to the rate of change of the function represented in the table."
So, the complete statement is: The rate of change in the function [tex]\( y = x + 4 \)[/tex] is equal to the rate of change of the function represented in the table.
