Consider the linear function that is represented by the equation y = negative 10 x + 6 and the linear function that is represented by the equation y minus 36 = 8 (x minus 4). Which statement is correct regarding their slopes and y-intercepts?

To compare the slopes and y-intercepts of the two functions, we first rewrite both equations in the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

1. The first equation is already in slope-intercept form:
\( y = -10x + 6 \)
- Slope (m) = -10
- Y-intercept (b) = 6

2. Now, let's rewrite the second equation \( y - 36 = 8(x - 4) \):
- Distributing on the right side:
\[ y - 36 = 8x - 32 \]
- Adding 36 to both sides to solve for y:
\[ y = 8x - 32 + 36 \]
\[ y = 8x + 4 \]
- Now we have:
- Slope (m) = 8
- Y-intercept (b) = 4

Now, we can compare the slopes and y-intercepts:

- **Slopes**:
- The slope of the first function is -10.
- The slope of the second function is 8.
- Since the absolute value of -10 (which is 10) is greater than 8, the first function has a steeper slope.

- **Y-intercepts**:
- The y-intercept of the first function is 6.
- The y-intercept of the second function is 4.
- Since 6 is greater than 4, the first function has a greater y-intercept.

Based on this comparison, the correct statement is:

**The function that is represented by the equation \( y = -10x + 6 \) has a steeper slope and a greater y-intercept.**