Question
Which function has greater rate of change?
I) y + 2 = 4(x + 3)
II) 4x + 2y = 6
I) y + 2 = 4(x + 3)
II) 4x + 2y = 6
Answers
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To determine the rate of change of each function, we need to get both functions in slope-intercept form, y = mx + b.
Starting with function I:
y + 2 = 4(x + 3)
y + 2 = 4x + 12
y = 4x + 10
Now, function II:
4x + 2y = 6
2y = -4x + 6
y = -2x + 3
In both cases, the coefficient of x (the number multiplying x) represents the rate of change.
So for function I, the rate of change is 4, and for function II, the rate of change is -2.
Since the rate of change represents how quickly y changes with respect to x, a larger absolute value indicates a greater rate of change.
Therefore, the function with the greater rate of change is function I).
Starting with function I:
y + 2 = 4(x + 3)
y + 2 = 4x + 12
y = 4x + 10
Now, function II:
4x + 2y = 6
2y = -4x + 6
y = -2x + 3
In both cases, the coefficient of x (the number multiplying x) represents the rate of change.
So for function I, the rate of change is 4, and for function II, the rate of change is -2.
Since the rate of change represents how quickly y changes with respect to x, a larger absolute value indicates a greater rate of change.
Therefore, the function with the greater rate of change is function I).
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