Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Question

Linear Function 1: y=7x+4

Linear Function 2:
x y

10 61
12 73

Linear Function ? has the lesser rate of change.

Answer 1

To compare the rates of change of the two linear functions, we first need to determine the slope (rate of change) of each function.

Linear Function 1 is given as: \[ y = 7x + 4 \] The rate of change (slope) is the coefficient of \(x\), which is \(7\).

Linear Function 2 is represented by points (10, 61) and (12, 73). We can calculate the slope using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the values:

• \((x_1, y_1) = (10, 61)\)
• \((x_2, y_2) = (12, 73)\)

This gives us: \[ \text{slope} = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6 \]

Now we can compare the slopes:

• Rate of change for Linear Function 1: \(7\)
• Rate of change for Linear Function 2: \(6\)

Since \(6 < 7\), Linear Function 2 has the lesser rate of change.

Therefore, the answer is: 2.