\begin{tabular}{|c|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 & 4 \\
\hline
[tex]$g(x)$[/tex] & -3 & -1 & 1 & 3 & 5 \\
\hline
\end{tabular}

Determine the slope of [tex]$g$[/tex].



Answer :

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]