The equation you've given is \( y = -\frac{x}{4} + 8 \). This represents a straight line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Key features of the line:

1. **Slope (m)**: The slope of the line is \( -\frac{1}{4} \). This means the line decreases by 1 unit for every 4 units it moves to the right.
   
2. **Y-intercept (b)**: The y-intercept is \( 8 \), which means the line crosses the y-axis at the point \( (0, 8) \).

3. **X-intercept**: To find the x-intercept, set \( y = 0 \) and solve for \( x \):
   \[
   0 = -\frac{x}{4} + 8
   \]
   Solving for \( x \), we get:
   \[
   \frac{x}{4} = 8 \quad \Rightarrow \quad x = 32
   \]
   So, the x-intercept is \( (32, 0) \).

### Graphical Representation:
- The line starts at \( (0, 8) \) on the y-axis and slopes downward at a rate of \( -\frac{1}{4} \), crossing the x-axis at \( (32, 0) \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you plot the graph of \( y = -\frac{x}{4} + 8 \)?
2. What happens to the slope if we change the equation to \( y = -\frac{x}{2} + 8 \)?
3. How would the line shift if the constant 8 were replaced by another number?
4. How do you find the point of intersection between two lines?
5. What is the general form of a linear equation, and how can you convert between forms?

**Tip**: Always remember that a negative slope means the line is decreasing as you move from left to right!

Explore the solution to the linear equation y = -x/4 + 8, including key concepts like slope, x-intercept, and y-intercept. Understand how to calculate the intercepts and how the slope affects the graph. 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