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.