https://file.aiquickdraw.com/mathbot/file/1728442616120xazv88kc.jpg

To find the output when the input is \( n \) for the given linear function, we first need to determine the pattern in the table.

### Table:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Input} & 1 & 2 & 3 & 4 & n \\
\hline
\text{Output} & -10 & -12 & -14 & -16 & ? \\
\hline
\end{array}
\]

### Step 1: Identify the pattern
- From \( \text{Input} = 1 \) to \( \text{Input} = 2 \), the output decreases by 2.
- Similarly, from \( \text{Input} = 2 \) to \( \text{Input} = 3 \), and from \( 3 \) to \( 4 \), the output decreases by 2 each time.

This suggests the function is linear with a constant rate of change (slope) of \( -2 \).

### Step 2: Find the function rule
Given that the slope \( m \) is \( -2 \), we can express the linear function as:
\[
y = mx + b
\]
Where \( m = -2 \) and \( b \) is the y-intercept.

To find \( b \), use one of the points from the table. Let's use the point \( (1, -10) \):
\[
-10 = -2(1) + b
\]
\[
b = -10 + 2 = -8
\]
So, the equation of the function is:
\[
y = -2x - 8
\]

### Step 3: Find the output when input is \( n \)
Substitute \( x = n \) into the function:
\[
y = -2n - 8
\]
Thus, the output when the input is \( n \) is \( -2n - 8 \).

Let me know if you'd like any additional details or have any questions!

---

**5 Questions to Expand Understanding:**
1. How do you determine the slope of a linear function from a table of values?
2. What is the role of the y-intercept in a linear equation?
3. Can this method be applied to non-linear functions? Why or why not?
4. How would the output change if the slope were positive instead of negative?
5. How do you graph a linear function from an equation?

**Tip:** Always check the difference between consecutive outputs to verify if a function is linear.

A table of values of a linear function is shown below. Find the output when the input is n.

Learn how to solve a linear function where the input is n and the output follows a consistent pattern. This problem involves identifying the linear equation and applying the slope-intercept form to find the output. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation