To find the slope of the line represented by the equation \(x + 2y = 20\), we'll first rewrite it in the slope-intercept form \(y = mx + b\), where \(m\) is the slope.

### Steps:
1. Start with the given equation: 
   \[
   x + 2y = 20
   \]
2. Solve for \(y\) by isolating it on one side:
   \[
   2y = -x + 20
   \]
3. Divide both sides by 2:
   \[
   y = -\frac{1}{2}x + 10
   \]

Now, the equation is in the form \(y = mx + b\), where the slope \(m = -\frac{1}{2}\).

### Conclusion:
The slope of the line is \(m = -\frac{1}{2}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the y-intercept of the line \(x + 2y = 20\)?
2. How would the graph of the line \(x + 2y = 20\) look?
3. How do you find the slope between two points on a line?
4. What happens to the slope if the line is vertical or horizontal?
5. How do parallel and perpendicular lines relate to slope?

**Tip:** The slope represents how steep a line is. Negative slopes mean the line is falling from left to right.

Learn how to find the slope of the linear equation x + 2y = 20 by transforming it into the slope-intercept form. This step-by-step solution covers algebraic concepts like isolating variables and identifying the slope. 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