To determine which linear function has a greater rate of change, we need to calculate the rate of change (slope) for both functions.
Linear Function 1
The two points provided are (2, 12) and (1, 9).
The formula for the rate of change (slope) between two points (x₁, y₁) and (x₂, y₂) is given by:
\[ \text{Rate of Change} = \frac{y₂ - y₁}{x₂ - x₁} \]
Using the points:
- \( (x₁, y₁) = (1, 9) \)
- \( (x₂, y₂) = (2, 12) \)
Substituting in:
\[ \text{Rate of Change} = \frac{12 - 9}{2 - 1} = \frac{3}{1} = 3 \]
So, the rate of change for Linear Function 1 is 3.
Linear Function 2
The two points given for Linear Function 2 are (0, 2) and (5, 42).
Using the same formula:
\[ \text{Rate of Change} = \frac{y₂ - y₁}{x₂ - x₁} \]
Using the points:
- \( (x₁, y₁) = (0, 2) \)
- \( (x₂, y₂) = (5, 42) \)
Substituting in:
\[ \text{Rate of Change} = \frac{42 - 2}{5 - 0} = \frac{40}{5} = 8 \]
So, the rate of change for Linear Function 2 is 8.
Comparison
- Linear Function 1 has a rate of change of 3.
- Linear Function 2 has a rate of change of 8.
Since 8 is greater than 3, the conclusion is:
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
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