Math Problem Statement
Assuming a linear relationship, find the missing value in the table below. x: {1, 2, 3, 4, 5}, y: {5, 14, 23, 32, ?}
Solution
To find the missing value in the table assuming a linear relationship, we need to find a pattern or formula that connects the -values to the -values. The table is given as:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Relationships
Algebra
Arithmetic Sequence
Formulas
Linear Equation: y = mx + c
Theorems
Linear Growth
Slope Formula
Suitable Grade Level
Grades 6-8