To find the slope of the function [tex]\( g(x) \)[/tex] given the table of values:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 \\
\hline
g(x) & -3 & -1 & 1 & 3 & 5 \\
\hline
\end{array}
\][/tex]
we can use the slope formula for a linear function, which is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
1. First, select any two points from the table. Let's choose the points [tex]\( (0, -3) \)[/tex] and [tex]\( (1, -1) \)[/tex].
2. Assign the coordinates:
- [tex]\( (x_1, y_1) = (0, -3) \)[/tex]
- [tex]\( (x_2, y_2) = (1, -1) \)[/tex]
3. Apply these points to the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
4. Substitute the values into the formula:
[tex]\[
\text{slope} = \frac{-1 - (-3)}{1 - 0}
\][/tex]
5. Simplify the numerator:
[tex]\[
-1 - (-3) = -1 + 3 = 2
\][/tex]
6. Simplify the fraction:
[tex]\[
\text{slope} = \frac{2}{1} = 2.0
\][/tex]
Therefore, the slope of the function [tex]\( g \)[/tex] is:
[tex]\[
\boxed{2.0}
\][/tex]
