Given the following linear function, fill in the values for the function in the given table:
f(x)=0.25x+14

x
0	4	
functionsequation editor	8	10	
functionsequation editor
  f(x)
  	
functionsequation editor	1.25	1.75	
functionsequation editor	
functionsequation editor	3.25

To solve this problem, we need to evaluate the given linear function \( f(x) = 0.25x + 14 \) for the corresponding values of \( x \) from the table. The function is applied by substituting the \( x \)-values into the equation and solving for \( f(x) \).

Here's the table with filled-in values:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & f(0) = 0.25(0) + 14 = 14 \\
4 & f(4) = 0.25(4) + 14 = 15 \\
8 & f(8) = 0.25(8) + 14 = 16 \\
10 & f(10) = 0.25(10) + 14 = 16.5 \\
1.25 & f(1.25) = 0.25(1.25) + 14 = 14.3125 \\
1.75 & f(1.75) = 0.25(1.75) + 14 = 14.4375 \\
3.25 & f(3.25) = 0.25(3.25) + 14 = 14.8125 \\
\hline
\end{array}
\]

Would you like further explanation on any of these steps?

Here are 5 related questions to extend this topic:
1. What is the slope of the linear function \( f(x) = 0.25x + 14 \)?
2. How would you graph the linear function \( f(x) = 0.25x + 14 \)?
3. What is the \( y \)-intercept of the function \( f(x) = 0.25x + 14 \)?
4. How would the function change if the slope were doubled?
5. What is the significance of the slope in real-world applications of linear functions?

**Tip:** When solving linear functions, always substitute the \( x \)-value into the equation carefully to avoid mistakes in calculation.

Given the following linear function, fill in the values for the function in the given table: f(x) = 0.25x + 14

Learn how to evaluate the linear function f(x) = 0.25x + 14 by filling in the values in the table. This problem focuses on applying the linear function formula and understanding the slope-intercept form, suitable for students in Grades 6-8.

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