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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
3x+y=10 and you need to solve for y
![### Solving Equations: Writing in Function Form
**Problem Statement:**
1. Rewrite the equation into function form. (Solve for \( y \))
\[ 3x + y = 10 \]
**Solution Steps:**
1. **Identify the given equation:**
- The equation to be solved is \( 3x + y = 10 \).
2. **Isolate the variable \( y \):**
- To convert the equation into function form (also known as the slope-intercept form), solve for \( y \).
3. **Subtract \( 3x \) from both sides:**
\[
y = -3x + 10
\]
4. **Final Function Form:**
- The equation in function form is \( y = -3x + 10 \).
**Explanation:**
- **Function form,** or slope-intercept form, is written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- In this example, \( m = -3 \) and \( b = 10 \).
This converted equation can be used to easily graph the line on a coordinate plane, where the slope (\(-3\)) represents the steepness of the line and the y-intercept (\(10\)) indicates the point where the line crosses the y-axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07d49b6d-0b8b-4fb0-8890-d011518a6909%2F71a67e8f-f9a4-450e-a477-d1f39de6eeb4%2Fgm2ejat_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Equations: Writing in Function Form
**Problem Statement:**
1. Rewrite the equation into function form. (Solve for \( y \))
\[ 3x + y = 10 \]
**Solution Steps:**
1. **Identify the given equation:**
- The equation to be solved is \( 3x + y = 10 \).
2. **Isolate the variable \( y \):**
- To convert the equation into function form (also known as the slope-intercept form), solve for \( y \).
3. **Subtract \( 3x \) from both sides:**
\[
y = -3x + 10
\]
4. **Final Function Form:**
- The equation in function form is \( y = -3x + 10 \).
**Explanation:**
- **Function form,** or slope-intercept form, is written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- In this example, \( m = -3 \) and \( b = 10 \).
This converted equation can be used to easily graph the line on a coordinate plane, where the slope (\(-3\)) represents the steepness of the line and the y-intercept (\(10\)) indicates the point where the line crosses the y-axis.
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