Which expression can be used to determine the slope of the linear function represented in the table?

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
0 & 5 \\
\hline
4 & 9 \\
\hline
\end{tabular}

A. [tex]$\frac{9-5}{4-0}$[/tex]

B. [tex]$\frac{4-0}{9-5}$[/tex]

C. [tex]$\frac{5-0}{9-4}$[/tex]

D. [tex]$\frac{9-4}{5-0}$[/tex]



Answer :

To determine the expression that calculates the slope of the linear function represented by the given table, follow these steps:

1. Identify the coordinates: From the table,
- The coordinates of the first point are [tex]\((0, 5)\)[/tex].
- The coordinates of the second point are [tex]\((4, 9)\)[/tex].

2. Recall the slope formula: The slope [tex]\( m \)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

3. Substitute the values:
- Here, [tex]\( x_1 = 0 \)[/tex], [tex]\( y_1 = 5 \)[/tex], [tex]\( x_2 = 4 \)[/tex], and [tex]\( y_2 = 9 \)[/tex].
- Substitute these values into the slope formula:
[tex]\[ m = \frac{9 - 5}{4 - 0} \][/tex]

4. Simplify the expression:
[tex]\[ m = \frac{9 - 5}{4 - 0} = \frac{4}{4} = 1.0 \][/tex]

5. Match the expression with the given options:
- The correct expression to determine the slope is [tex]\(\frac{9-5}{4-0}\)[/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]