To determine which linear function has the lesser rate of change, we first need to identify the rates of change of both functions.
Linear Function 1: \( y = 7x + 4 \)
The rate of change (slope) is the coefficient of \( x \), which is 7.
Linear Function 2: We need to calculate the rate of change between 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:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (10, 61) and (12, 73):
- \(x_1 = 10\), \(y_1 = 61\)
- \(x_2 = 12\), \(y_2 = 73\)
Calculating the slope:
\[ \text{slope} = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6 \]
Now we can compare the rates of change:
- Linear Function 1 Rate of Change: 7
- Linear Function 2 Rate of Change: 6
Since 6 < 7, Linear Function 2 has the lesser rate of change.
So the answer is:
2