Math Problem Statement
Assuming a linear relationship, find the missing value in the table below.
Solution
To find the missing value in the table under the assumption of a linear relationship, we need to determine the relationship between the and values.
Step 1: Identify the pattern in the change of .
We are given:
x & 1 & 2 & 3 & 4 & 5 \\ y & 7 & 16 & 25 & 34 & ? \\ \end{array}$$ To verify if this is a linear relationship, we can check the difference between consecutive $$y$$-values. - $$16 - 7 = 9$$ - $$25 - 16 = 9$$ - $$34 - 25 = 9$$ Since the difference between consecutive $$y$$-values is constant (equal to 9), we have a **linear relationship**. ### Step 2: Find the missing value. The difference between consecutive $$y$$-values is 9, so we can find the missing value for $$x = 5$$ by adding 9 to the last known value of $$y$$ when $$x = 4$$: $$34 + 9 = 43$$ Thus, the missing value is $$\boxed{43}$$. Would you like further clarification on any step, or more details? ### Additional Questions: 1. What is the equation for the linear relationship in this example? 2. How would you extend this pattern for $$x = 6$$? 3. Can we generalize a formula for any $$x$$ value based on this pattern? 4. How can you check if a set of points has a linear relationship? 5. What role does the slope play in a linear equation? ### Tip: When analyzing linear relationships, always check for constant differences between consecutive terms to confirm the linearity!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
y = mx + b (Equation of a straight line)
Theorems
Constant difference theorem for linear relationships
Suitable Grade Level
Grades 6-8