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