How do the consecutive terms relate to each other?
Type of Function: Linear Function: y=1/2x+5/2
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
1
y
1
1.5
2
2.5
3
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 (0,2.5) and (1,3). We will start by substituting 0 and 2.5 for x and y, respectively.
We can write a partial equation of the function represented by the table.
y=mx+2.5
To find the value of m, we will substitute 1 for x and 3 for y in our partial equation.
