1. Rewrite the equation into function form. (Solve for y) 3x +y = 10

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
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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