Find the formula for a linear function f that models the data in the table exactly -2 4 f(x) 13 6 -1 -8 f(x) =D (Simplify your answer. Do not factor. Use integers or fractions for any numbers
Find the formula for a linear function f that models the data in the table exactly -2 4 f(x) 13 6 -1 -8 f(x) =D (Simplify your answer. Do not factor. Use integers or fractions for any numbers
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Find the Formula for a Linear Function**
Objective: Determine the formula for a linear function \( f \) that exactly models the data provided in the table.
**Data Table:**
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
f(x) & 13 & 6 & -1 & -8 \\
\hline
\end{array}
\]
### Steps to Follow:
1. **Identify the Slope (\(m\)):**
- Use the formula for slope between two points:
\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
2. **Use Point-Slope Form to Derive the Equation:**
- Once the slope is identified, use the point-slope form:
\[
y - f(x_1) = m(x - x_1)
\]
- Simplify to get the linear equation in slope-intercept form (\(y = mx + b\)).
3. **Verify with Other Points:**
- Check that the derived equation fits all data points from the table.
### Additional Instructions:
- Simplify your answer. Do not factor. Use integers or fractions for any numbers in the expressions.
**Input:**
- Enter the derived formula in the answer box and click "Check Answer" to validate.
This exercise reinforces understanding of linear functions and slope-intercept form application in model fitting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9363fbf8-1ca8-4725-9136-263a3c8a662e%2F224eb634-130b-4b09-bdeb-93d4e32bb96a%2Frr0fvr1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Formula for a Linear Function**
Objective: Determine the formula for a linear function \( f \) that exactly models the data provided in the table.
**Data Table:**
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
f(x) & 13 & 6 & -1 & -8 \\
\hline
\end{array}
\]
### Steps to Follow:
1. **Identify the Slope (\(m\)):**
- Use the formula for slope between two points:
\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
2. **Use Point-Slope Form to Derive the Equation:**
- Once the slope is identified, use the point-slope form:
\[
y - f(x_1) = m(x - x_1)
\]
- Simplify to get the linear equation in slope-intercept form (\(y = mx + b\)).
3. **Verify with Other Points:**
- Check that the derived equation fits all data points from the table.
### Additional Instructions:
- Simplify your answer. Do not factor. Use integers or fractions for any numbers in the expressions.
**Input:**
- Enter the derived formula in the answer box and click "Check Answer" to validate.
This exercise reinforces understanding of linear functions and slope-intercept form application in model fitting.
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