To find the missing value in the table assuming a linear relationship between $x$ and $y$, we can start by identifying the pattern or relationship between the values.

Given dataTo find the missing value in the table assuming a linear relationship between $x$ and $y$, we can start by identifying the pattern or relationship between the values.

Given

y & 1 & 2 & 3 & 4 & 5 \\ \hline x & 3 & 13 & 23 & 33 & ? \\ \end{array}$$ ### Step 1: Identify the Pattern The change in $$x$$ for each increment in $$y$$ appears to be constant. Let's calculate the difference between consecutive $$x$$ values: $$\begin{aligned} \Delta x_1 & = 13 - 3 = 10, \\ \Delta x_2 & = 23 - 13 = 10, \\ \Delta x_3 & = 33 - 23 = 10. \end{aligned}$$ This indicates that the difference between consecutive $$x$$ values is 10. ### Step 2: Find the Missing Value Since the pattern is consistent, we can find the missing value for $$y = 5$$ by adding 10 to the previous $$x$$ value: $$x_5 = 33 + 10 = 43.$$ ### Final Answer The missing value in the table for $$y = 5$$ is $$x = 43$$. Would you like more details or have any questions? Here are some related questions you might find helpful: 1. What is the equation of the line that represents the relationship between $$x$$ and $$y$$? 2. How would you determine the missing value if the relationship wasn't linear? 3. What is the slope of the line in this linear relationship? 4. How do you interpret the slope in this context? 5. Can you find the value of $$y$$ if $$x = 53$$? **Tip:** When dealing with linear relationships, always check for a constant difference between values, as it can simplify finding missing data points.