Question

Which of the relationships below represents a function with the same rate of change as the function y, equals, 4, x, minus, 5y=4x−5?
A
x
y
B
x
y
C
xx yy
minus, 4−4 11
00 minus, 5−5
44 minus, 11−11
88 minus, 17−17
D
xx yy
minus, 1−1 minus, 6−6
11 minus, 4−4
33 minus, 2−2
55 00
Answer
Multiple Choice Answers
AA
BB
CC
DD

Answer 1

To determine which relationship among the provided options represents a function with the same rate of change as the function given by the equation \( y = 4x - 5 \), we first need to find the slope (rate of change) of this function.

The function \( y = 4x - 5 \) is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope. Here, the slope \( m = 4 \).

Next, we need to inspect the provided options and calculate the slope for each set of points to see if any has the same slope of 4.

### Analyzing Options:

**Option A:**
- Points: \( (-4, 11) \), \( (0, -5) \)
- Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 11}{0 - (-4)} = \frac{-16}{4} = -4 \)

**Option B:**
- Points: (not provided clearly in the text)
- Please provide points to check further.

**Option C:**
- Points: \( (-4, 11) \), \( (0, -5) \), \( (4, -11) \), \( (8, -17) \)
- Slope between \( (-4, 11) \) and \( (0, -5) \):
- \( m = \frac{-5 - 11}{0 - (-4)} = \frac{-16}{4} = -4 \)
- Slope between \( (0, -5) \) and \( (4, -11) \):
- \( m = \frac{-11 - (-5)}{4 - 0} = \frac{-6}{4} = -\frac{3}{2} \)
- Slope between \( (4, -11) \) and \( (8, -17) \):
- \( m = \frac{-17 - (-11)}{8 - 4} = \frac{-6}{4} = -\frac{3}{2} \)

**Option D:**
- Points: \( (-1, -6) \), \( (1, -4) \), \( (3, -2) \), \( (5, 0) \)
- Slope between \( (-1, -6) \) and \( (1, -4) \):
- \( m = \frac{-4 - (-6)}{1 - (-1)} = \frac{2}{2} = 1 \)
- Slope between \( (1, -4) \) and \( (3, -2) \):
- \( m = \frac{-2 - (-4)}{3 - 1} = \frac{2}{2} = 1 \)
- Slope between \( (3, -2) \) and \( (5, 0) \):
- \( m = \frac{0 - (-2)}{5 - 3} = \frac{2}{2} = 1 \)

### Conclusion
None of the options provided a slope of 4. The calculations for each option show that none have the same steepness as the line \( y = 4x - 5 \). If the points for Option B were provided, it would be essential to check those as well.

No option corresponds to a function with the same rate of change (slope) as \( y = 4x - 5 \). Please verify or provide more options to evaluate.