How do the consecutive terms relate to each other?
Type of Function: Linear Function: y=0.2x-8.4
Practice makes perfect
Finding the Model
We want to tell whether the table of values represents a linear, exponential, or quadratic function. To do so, we will analyze how the consecutive terms are related to each other.
x
-3
-2
-1
0
y
-8.8
-8.6
-8.4
-8.2
Let's begin with calculating the first differences.
Since the first differences are all equal, the table of values represents a linear function.
Finding the Equation
Let's recall the slope-intercept form of this type of function.
y=mx+b
We will use two ordered pairs given in the table to find the values of m and b. For simplicity, let's use (0,-8.2) and (-1,-8.4). We will start by substituting 0 and -8.2 for x and y, respectively.
We can write a partial equation of the function represented by the table.
y=mx-8.2
To find the value of m, we will substitute -1 for x and -8.4 for y in our partial equation.
