A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, 7).

Question

What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change is Choose... ~ and the initial value is Choose... ~

Answer 1

To find the rate of change and the initial value of the linear function between the points A(0, 3) and B(2, 7), we can use the following formulas:

1. Rate of Change (slope) = \( \frac{y_2 - y_1}{x_2 - x_1} \)
2. Initial Value (y-intercept) = value of y when x = 0

Let's calculate the rate of change:

• Let \( (x_1, y_1) = (0, 3) \) and \( (x_2, y_2) = (2, 7) \)

Rate of change: \[ \text{Rate of Change} = \frac{7 - 3}{2 - 0} = \frac{4}{2} = 2 \]

Next, the initial value (y-intercept) is the y-coordinate when x is 0, which is given as 3 in point A(0, 3).

Thus we can complete the statements:

• The rate of change is 2,
• and the initial value is 3.

So, The rate of change is 2 and the initial value is 3.