To determine which linear function has the lesser rate of change, we first need to identify the rate of change for both functions.
Linear Function 1: The equation is given as \( y = 7x + 4 \). The rate of change (slope) here is 7.
Linear Function 2: To find the rate of change (slope), we need to use the given points (10, 61) and (12, 73). The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the values:
- \( x_1 = 10, y_1 = 61 \)
- \( x_2 = 12, y_2 = 73 \)
We calculate as follows:
\[ \text{slope} = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6 \]
Now we have the rates of change:
- Linear Function 1 has a rate of change of 7.
- Linear Function 2 has a rate of change of 6.
Comparison: Since 6 (from Linear Function 2) is less than 7 (from Linear Function 1), Linear Function 2 has the lesser rate of change.
Conclusion: Linear Function 2 has the lesser rate of change. Therefore, the answer is:
2