Answer:
The rate of change is -4.5 and the relation of the table is a linear function
Step-by-step 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:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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):
[tex]\displaystyle m=\frac{78.5-83}{3-2}=-4.5[/tex]
Now for (7,60.5) and (14,29):
[tex]\displaystyle m=\frac{29-60.5}{14-7}=\frac{-31.5}{7}=-4.5[/tex]
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.
