https://file.aiquickdraw.com/mathbot/file/1726808410973qfamk8en.jpg

To find the missing value in the table assuming a linear relationship, we need to find a pattern or formula that connects the \(x\)-values to the \(y\)-values. The table is given as:

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 \\
\hline
y & 5 & 14 & 23 & 32 & ? \\
\hline
\end{array}
\]

### Step-by-Step Solution:
1. **Find the pattern in the \(y\)-values:**
   Let's calculate the difference between consecutive \(y\)-values:
   \[
   14 - 5 = 9
   \]
   \[
   23 - 14 = 9
   \]
   \[
   32 - 23 = 9
   \]
   The difference between consecutive \(y\)-values is consistently 9. This indicates a linear relationship with a slope of 9.

2. **Determine the linear equation:**
   A linear equation has the form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.
   - We already found \(m = 9\).
   - To find \(c\), we can use any pair of \( (x, y) \). Let's use \( (1, 5) \):
     \[
     5 = 9 \cdot 1 + c \Rightarrow c = 5 - 9 = -4
     \]

   So, the linear equation is:
   \[
   y = 9x - 4
   \]

3. **Find the missing value when \( x = 5 \):**
   \[
   y = 9(5) - 4 = 45 - 4 = 41
   \]

Therefore, the missing value for \( y \) when \( x = 5 \) is **41**.

Would you like more details on any step, or have any questions? Here are some related questions:

1. How do you find the slope of a linear relationship from a table of values?
2. What is the significance of the y-intercept in a linear equation?
3. How would the equation change if the values in the table were not linear?
4. How do you verify if a relationship is linear using a table of values?
5. Can you explain the method to derive a linear equation from two given points?

**Tip:** Always check the differences between consecutive y-values to identify a linear relationship in a table.

Assuming a linear relationship, find the missing value in the table below. x: {1, 2, 3, 4, 5}, y: {5, 14, 23, 32, ?}

Learn how to find the missing value in a table by identifying the linear relationship between x and y. This problem involves understanding arithmetic sequences and using the linear equation y = mx + c. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation