To determine the slope of a linear function represented by the coordinates in a table, we use the formula for the slope [tex]\( m \)[/tex], which is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the values from the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 5 \\
\hline
4 & 9 \\
\hline
\end{array}
\][/tex]
We can identify the points as [tex]\((x_1, y_1) = (0, 5)\)[/tex] and [tex]\((x_2, y_2) = (4, 9)\)[/tex].
Plugging these values into the slope formula, we get:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 5}{4 - 0}
\][/tex]
Calculating the numerator and the denominator separately:
[tex]\[
9 - 5 = 4 \quad \text{and} \quad 4 - 0 = 4
\][/tex]
So the slope [tex]\( m \)[/tex] is:
[tex]\[
m = \frac{4}{4} = 1
\][/tex]
Therefore, the correct expression that can be used to determine the slope of the linear function represented in the table is:
[tex]\[
\frac{9-5}{4-0}
\][/tex]
