To determine the slope of the linear function represented by the ordered pairs [tex]\((6, 2)\)[/tex] and [tex]\((9, 8)\)[/tex], you should follow these steps:
1. Recall the formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
2. Substitute the given points into the formula. Here, [tex]\((x_1, y_1) = (6, 2)\)[/tex] and [tex]\((x_2, y_2) = (9, 8)\)[/tex].
[tex]\[
m = \frac{8 - 2}{9 - 6}
\][/tex]
3. Calculate the difference in the [tex]\(y\)[/tex]-coordinates ([tex]\(y_2 - y_1\)[/tex]):
[tex]\[
8 - 2 = 6
\][/tex]
4. Calculate the difference in the [tex]\(x\)[/tex]-coordinates ([tex]\(x_2 - x_1\)[/tex]):
[tex]\[
9 - 6 = 3
\][/tex]
5. Divide the difference in the [tex]\(y\)[/tex]-coordinates by the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[
m = \frac{6}{3} = 2
\][/tex]
Therefore, the slope of the function is [tex]\(2\)[/tex].
So, the answer is [tex]\(2\)[/tex].
