standard to slope intercept form worksheet

Converting equations from **standard form** to **slope-intercept form** is a common algebra task. Here’s a brief guide and worksheet to help practice these conversions.

### 1. **Understanding the Forms**:

- **Standard Form**: \( Ax + By = C \)
- **Slope-Intercept Form**: \( y = mx + b \)
  - Where \( m \) is the slope and \( b \) is the y-intercept.

### 2. **Steps to Convert**:

To convert from standard form \( Ax + By = C \) to slope-intercept form \( y = mx + b \):

1. **Isolate \( y \)**: Move the \( Ax \) term to the right side of the equation:  
   \( By = -Ax + C \)

2. **Solve for \( y \)** by dividing everything by \( B \):  
   \( y = -\frac{A}{B}x + \frac{C}{B} \)

Now, the equation is in slope-intercept form with slope \( m = -\frac{A}{B} \) and intercept \( b = \frac{C}{B} \).

### 3. **Worksheet: Convert the Following to Slope-Intercept Form**:

#### a. \( 3x + 2y = 12 \)

#### b. \( 4x - 5y = 20 \)

#### c. \( 2x + 7y = -14 \)

#### d. \( 5x + y = 8 \)

#### e. \( -2x + 3y = 6 \)

---

### 4. **Example Solutions**:

#### Example 1: Convert \( 3x + 2y = 12 \) to slope-intercept form.

1. Move \( 3x \) to the right side:  
   \( 2y = -3x + 12 \)

2. Divide by 2:  
   \( y = -\frac{3}{2}x + 6 \)

#### Example 2: Convert \( 5x + y = 8 \) to slope-intercept form.

1. Move \( 5x \) to the right side:  
   \( y = -5x + 8 \)

Now, try the worksheet problems!

---

Would you like the detailed solutions to the worksheet problems, or do you have any questions about these steps?

### 5 Related Practice Questions:

1. What is the slope of the equation \( 2x + 3y = 9 \) when converted to slope-intercept form?
2. How does the y-intercept change if \( C \) is doubled in \( Ax + By = C \)?
3. Convert \( 7x - 4y = 28 \) to slope-intercept form.
4. How do you determine if two lines are parallel using their slopes in slope-intercept form?
5. If given a slope-intercept form \( y = mx + b \), how do you convert it back to standard form?

**Tip**: Always simplify fractions in slope and intercept to keep your answer neat and readable.

Practice converting equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b) with this detailed worksheet. Learn how to isolate variables, calculate slope, and find the y-intercept. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation