https://file.aiquickdraw.com/mathbot/file/1726605067209fjoiabut.jpg

To find the slope and the y-intercept of the line represented by the equation \( 5x + 2y = 12 \), we need to rewrite the equation in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Solve for \( y \)
Start by isolating \( y \) on one side of the equation.

\[
5x + 2y = 12
\]

Subtract \( 5x \) from both sides:

\[
2y = -5x + 12
\]

### Step 2: Divide by 2
Now divide both sides by 2 to solve for \( y \):

\[
y = -\frac{5}{2}x + 6
\]

### Final Equation
The equation in slope-intercept form is:

\[
y = -\frac{5}{2}x + 6
\]

### Results:
- **Slope** (\( m \)): \( -\frac{5}{2} \)
- **Y-intercept** (\( b \)): \( 6 \)

Would you like any additional details or have any questions?

---

Here are 5 related questions to expand your understanding:
1. How would the slope change if the coefficient of \( x \) in the original equation was positive?
2. What does the slope tell you about the direction of the line on the graph?
3. Can you find the x-intercept of this line by setting \( y = 0 \)?
4. How would you graph this line using the slope and y-intercept?
5. If the equation were \( 5x + 2y = -12 \), how would the slope and y-intercept change?

**Tip**: When writing linear equations, always aim to express them in slope-intercept form \( y = mx + b \) for easy identification of the slope and intercepts.

Find the slope and the y-intercept of the line 5x + 2y = 12

Learn how to determine the slope and y-intercept of the linear equation 5x + 2y = 12. This tutorial guides you through rewriting the equation into the slope-intercept form and calculating the slope and y-intercept, essential skills in algebra 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