Question

A line in the coordinate plane passes through the points(9, 3)and(6, 10).

What are the rate of change and the initial value of the function modeled by the line?

Answer 1

Average rate of change is -7/3 and the initial value is 24

Explanation:

The rate of change is simply the slope of the line connecting the points

mathematically, that would be;

m = y2-y1/x2-x1

m = (10-3)/(6-9) = -7/3

Let us get the complete equation;

The general equation form is;

y = mx + b

where m is slope and b is y-intercept

y = -7x/3 + b

To get b, we simply insert one of the points

Let us use (9,3)

We insert x = 9 and y = 3

So we have;

3 = -21 + b

b = 3 + 21

b = 24

So the complete equation is;

y = -7x/3 + 24

The initial value is when x = 0

If x = 0, y will be 24