Let's determine which function has a greater slope by comparing the slopes of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] step-by-step.
### Step 1: Determine the slope of [tex]\( f(x) \)[/tex]
The function [tex]\( f(x) = 4x + 10 \)[/tex] is a linear function of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope. Here, [tex]\( m = 4 \)[/tex]. Therefore, the slope of [tex]\( f(x) \)[/tex] is 4.
### Step 2: Determine the slope of [tex]\( g(x) \)[/tex]
To determine the slope of [tex]\( g(x) \)[/tex], we can use the given points from the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
2 & 5 \\
\hline
4 & 7 \\
\hline
6 & 9 \\
\hline
\end{array}
\][/tex]
The slope of a function between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's use the first two points [tex]\((2, 5)\)[/tex] and [tex]\((4, 7)\)[/tex] to find the slope of [tex]\( g(x) \)[/tex]:
[tex]\[
\text{slope of } g(x) = \frac{7 - 5}{4 - 2} = \frac{2}{2} = 1
\][/tex]
### Step 3: Compare the slopes
We now have:
- The slope of [tex]\( f(x) \)[/tex] is 4.
- The slope of [tex]\( g(x) \)[/tex] is 1.
Since [tex]\( 4 > 1 \)[/tex], the slope of [tex]\( f(x) \)[/tex] is greater than the slope of [tex]\( g(x) \)[/tex].
### Conclusion
Based on the comparison, the function [tex]\( f(x) \)[/tex] has a greater slope.
Thus, the correct statement is:
[tex]\( f(x) \)[/tex] has a greater slope.
