To determine the type of the function, find the differences of successive y-values.
Type of Function: Linear Function: y=0.5x+3
Practice makes perfect
Let's first determine the type of function that best models the height of a plant, and then use the general form of this type to write a function.
Determining the Type of Function
We start by finding the differences of successive y-values, namely the first differences.
We see that the differences are all equal meaning the table represents a linear function.
Writing the Function
We can model the height y of the plant after x week by using a linear function.
y=mx+b
Here, m is the slope and b is the y-intercept. From the table, we see that the y-intercept is 3. Let's put this into the equation using substitution.
y=mx+b
⇕
y=mx+3
We can find the slope m by substituting an ordered pair in the table. Let's substitute (2,4).
