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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Question
![**Task: Find a Formula for the Linear Function**
**Problem Statement:**
You are given a linear function \( g(x) \), and two conditions:
- \( g(150) = 2130 \)
- \( g(360) = 3390 \)
Your task is to find the formula for \( g(x) \).
**Note:** Enter the exact answer in the provided input box.
**Solution Steps:**
To find the formula for the linear function \( g(x) \), consider the following steps:
1. **Identify the Slope (m):**
- The slope of a linear function can be found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Using the given points \((150, 2130)\) and \((360, 3390)\):
\[
m = \frac{3390 - 2130}{360 - 150} = \frac{1260}{210} = 6
\]
2. **Write the Equation Using Point-Slope Form:**
- The point-slope form of a linear equation is:
\[
y - y_1 = m(x - x_1)
\]
- Using point \((150, 2130)\) and \(m = 6\):
\[
g(x) - 2130 = 6(x - 150)
\]
3. **Solve for \( g(x) \):**
- Expand and simplify:
\[
g(x) = 6x - 900 + 2130
\]
\[
g(x) = 6x + 1230
\]
**Final Function:**
The linear function is:
\[
g(x) = 6x + 1230
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ab3c20-a3cd-4c1e-8775-52ac5ed4d4cf%2F7a17468c-0f36-4c85-8e73-46869c0984db%2Fpqdxff_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Find a Formula for the Linear Function**
**Problem Statement:**
You are given a linear function \( g(x) \), and two conditions:
- \( g(150) = 2130 \)
- \( g(360) = 3390 \)
Your task is to find the formula for \( g(x) \).
**Note:** Enter the exact answer in the provided input box.
**Solution Steps:**
To find the formula for the linear function \( g(x) \), consider the following steps:
1. **Identify the Slope (m):**
- The slope of a linear function can be found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Using the given points \((150, 2130)\) and \((360, 3390)\):
\[
m = \frac{3390 - 2130}{360 - 150} = \frac{1260}{210} = 6
\]
2. **Write the Equation Using Point-Slope Form:**
- The point-slope form of a linear equation is:
\[
y - y_1 = m(x - x_1)
\]
- Using point \((150, 2130)\) and \(m = 6\):
\[
g(x) - 2130 = 6(x - 150)
\]
3. **Solve for \( g(x) \):**
- Expand and simplify:
\[
g(x) = 6x - 900 + 2130
\]
\[
g(x) = 6x + 1230
\]
**Final Function:**
The linear function is:
\[
g(x) = 6x + 1230
\]
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