consider the lines y=1/2x and y=4-8x which line has the greater slope and which line has the greater y-intercept?

To compare the lines \( y = \frac{1}{2}x \) and \( y = 4 - 8x \), we need to examine their slopes and y-intercepts.

1. **Slope:**
   - The slope of a line in the equation \( y = mx + b \) is given by \( m \).
   - For \( y = \frac{1}{2}x \), the slope is \( \frac{1}{2} \).
   - For \( y = 4 - 8x \), rewriting it as \( y = -8x + 4 \), the slope is \( -8 \).

   **Conclusion:**
   - The line \( y = \frac{1}{2}x \) has a slope of \( \frac{1}{2} \).
   - The line \( y = 4 - 8x \) has a slope of \( -8 \).
   - Therefore, the line \( y = \frac{1}{2}x \) has the **greater slope** (since \( \frac{1}{2} \) is larger than \( -8 \)).

2. **Y-intercept:**
   - The y-intercept in the equation \( y = mx + b \) is given by \( b \).
   - For \( y = \frac{1}{2}x \), the y-intercept is 0 (since there's no constant term).
   - For \( y = 4 - 8x \), the y-intercept is 4.

   **Conclusion:**
   - The line \( y = 4 - 8x \) has the **greater y-intercept** (4 compared to 0).

### Summary:
- The line with the **greater slope** is \( y = \frac{1}{2}x \).
- The line with the **greater y-intercept** is \( y = 4 - 8x \).

Would you like more details or further explanation on any part of this?

Here are 5 related questions:
1. How do you determine the slope of a line from its equation?
2. What does the slope tell us about the steepness of a line?
3. Can a line with a negative slope have a greater y-intercept?
4. How would you graph these two lines?
5. How do parallel lines compare in slope?

**Tip:** A line's slope represents its steepness, with positive slopes going upward from left to right and negative slopes going downward.

Consider the lines y = 1/2x and y = 4 - 8x. Which line has the greater slope and which line has the greater y-intercept?

Explore how to compare the slopes and y-intercepts of two linear equations, y = 1/2x and y = 4 - 8x. This problem helps students understand slope-intercept form and how to determine the slope and y-intercept from a linear equation. Suitable for Grades 8-10.

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