Question

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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).
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...

Explanation:

Step1: Calculate rate of change (slope)

The formula for slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(0, 3)\) and \((x_2, y_2)=(2, 7)\). So, \(m=\frac{7 - 3}{2 - 0}=\frac{4}{2}=2\).

Step2: Determine initial value

The initial value of a linear function (when it's in the form \(y = mx + b\)) is the \(y\)-intercept (\(b\)), which is the \(y\)-value when \(x = 0\). From point \(A(0, 3)\), when \(x = 0\), \(y = 3\), so the initial value is 3.

Answer:

The rate of change is \(2\) and the initial value is \(3\).