Start by determining the model using the first differences of the values of the given data.
y=3x-2
Practice makes perfect
We will start by determining the best model that fits the data. Then we will be able to write an exact equation that models the data.
Finding a Model
We want to model the given data set. Note that the x-values have a common difference of 1. Therefore, we can check if the y-values have a common difference, a common ratio, or constant second difference. It will tell us which model is most appropriate for the data set.
Let's start by checking our data set for a common difference!
We see that there is a common difference of 3, so a linear model fits the data.
Writing an Equation
We know that a linear function best models the data.
y=mx+b
To write an equation to model the data, we have to determine the values of the slope m and the y-intercept b. When x is 0, y is - 2. Therefore, b=- 2.
y=mx+b ⇔ y=mx -2
Let's now find m! We will use the Slope Formula and the points ( 0, - 2) and ( 1, 1).
