Question

can the scatter plot be fit exactly or only approximately by a linear function? how do you know?

x	y
3	6
5	7
7	8
9	9

choose the correct answer below.
a. the scatter plot can be fit exactly by a linear function because the first differences of the outputs are nearly constant.
b. the scatter plot can be fit exactly by a linear function because the first differences of the outputs are equal.
c. the scatter plot can only be fit approximately by a linear function because a straight line will pass through all points.
d. the scatter plot can only be fit approximately by a linear function because no straight line will fit all points.

Explanation:

Step1: Calculate first differences of y

$\Delta y_1 = 6-5=1$, $\Delta y_2=7-6=1$, $\Delta y_3=8-7=1$, $\Delta y_4=9-8=1$

Step2: Calculate first differences of x

$\Delta x_1 = 3-1=2$, $\Delta x_2=5-3=2$, $\Delta x_3=7-5=2$, $\Delta x_4=9-7=2$

Step3: Check linearity

Rate of change: $\frac{\Delta y}{\Delta x} = \frac{1}{2}$ (constant)

Answer:

B. The scatter plot can be fit exactly by a linear function because the first differences of the outputs are equal.