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]
