Math Problem Statement
Calculate the rate of change of the table:
X: [5, 10, 15, 20]
Y: [1, 5, 9, 13]
Solution
To calculate the rate of change from the table, we need to determine how much changes for every change in .
The table provides the following values:
\hline X & 5 & 10 & 15 & 20 \\ \hline Y & 1 & 5 & 9 & 13 \\ \hline \end{array}$$ The formula for the rate of change (slope) between two points is: $$\text{Rate of Change} = \frac{\Delta Y}{\Delta X} = \frac{Y_2 - Y_1}{X_2 - X_1}$$ Now, let's calculate the rate of change between different points: 1. From $$X = 5$$ to $$X = 10$$, and from $$Y = 1$$ to $$Y = 5$$: $$\frac{5 - 1}{10 - 5} = \frac{4}{5}$$ 2. From $$X = 10$$ to $$X = 15$$, and from $$Y = 5$$ to $$Y = 9$$: $$\frac{9 - 5}{15 - 10} = \frac{4}{5}$$ 3. From $$X = 15$$ to $$X = 20$$, and from $$Y = 9$$ to $$Y = 13$$: $$\frac{13 - 9}{20 - 15} = \frac{4}{5}$$ Since the rate of change is consistent at $$\frac{4}{5}$$ for all intervals, the correct answer is: $$\boxed{\frac{4}{5}}$$ Would you like any more details or have any other questions? Here are 5 related questions for further practice: 1. How do you interpret the rate of change in real-life scenarios? 2. What would the table look like if the rate of change were negative? 3. Can a table have a varying rate of change? How would you identify it? 4. What is the relationship between rate of change and the slope of a line? 5. How does the rate of change help in understanding linear functions? **Tip:** The rate of change (or slope) can be thought of as how steep a line is. A higher slope indicates a steeper line.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Rate of Change
Slope
Formulas
Rate of Change = (Y2 - Y1) / (X2 - X1)
Theorems
Slope formula for a linear function
Suitable Grade Level
Grade 8-10