Math Problem Statement
Construct a model representing the table's data if the function g(x) is approximately linear. Round to the thousandths place. The table gives selected inputs and outputs for a data set: x = {-6, -3, 4, 12} and g(x) = {-2, 5, 19, 32}.
Solution
To construct a linear model, , we need to find the slope and y-intercept using the given data points.
1. Calculate the slope ()
The formula for the slope between two points and is:
Using the data points and :
2. Calculate the y-intercept ()
We can use the slope and any point, say , to find :
3. Check the best approximation
After rounding and to the nearest thousandth, we have:
This matches the first answer choice.
Final Answer
The correct model is:
Would you like to explore further details or have any questions?
5 Related Questions
- How do you determine if a set of data points is linear?
- What is the formula for calculating the slope between two points?
- How do you find the y-intercept of a line using a point and the slope?
- Why is it important to round to the thousandths place in linear modeling?
- How do linear models help in predicting data trends?
Tip: Always choose two points with a wide range for accurate slope calculation to minimize rounding errors.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Algebra
Formulas
Slope formula: m = (g(x2) - g(x1)) / (x2 - x1)
Linear equation: g(x) = mx + b
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10