Question

What's the rate of change and is it a linear function​

Answer 1

The rate of change is -4.5 and the relation of the table is a linear function

Explanation:

Linear function.

A linear function can be identified because the rate of change is constant at every point of its domain.

The graph of a linear function is a straight line with a constant slope.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

We'll show the relation shown in the table is a linear function. We'll calculate the slope for any random pair of points. For example, using (2,83) and (3,78.5):

`\displaystyle m=(78.5-83)/(3-2)=-4.5`

Now for (7,60.5) and (14,29):

`\displaystyle m=(29-60.5)/(14-7)=(-31.5)/(7)=-4.5`

Proceeding in a similar way with any pair of points, the slope will always result in the same value, thus the rate of change is -4.5 and the relation of the table is a linear function.