Recognizing Linear and Exponential Data
The problem: For each table of data, find either a linear or exponential function that models the data.
Part a).

Notice that as each x increases by 1, each corresponding y increases by 1.5 (a constant amount). Thus, the data can be modeled by a linear function, f(x) = mx + b. Recall that m is the slope of the line and b is the yintercept. There are two ways to obtain the equation of this line.
1). The equation of the line can be determined symbolically
as follows:
Since each y increases by 1.5 when each x increases
by 1, m= 1.5.
Also, from the data point (0,  3) the yintercept can be identified as b
=  3. Thus, the equation is y = 1.5x  3
2). The equation of the line can be determined using the calculator
linear regression capability
as follows:
Press STAT then select EDIT. Enter the x values in
and the y values in .
Check the menu to
be sure that there are no functions listed and Plot1 is on (highlighted).
Press ZOOM and select 6 to graph points as a scatterplot
in the standard window [10,10,1] by [10,10,1]. Note that the data points
appear to lie in a straight line and the ydifferences calculated in L3 are equal. Whenever the ydifferences are all equal, a linear model will fit the data exactly.
Next press STAT, ARROW RIGHT to CALC, the select 4:LinReg(ax+b) by arrowing down to 4 and pressing ENTER . To copy the equation obtained into Y1, we press VARS followed by the RIGHT ARROW.
Then press ENTER three times.
The results show that the equation form is y=ax+b (same as y=mx+b),
where the slope a = 1.5 and the yintercept b = 3.
Thus, the result is y = 1.5x  3. To verify this visually,
graph the function, y = 1.5x  3, and the scatterplot
simultaneously.
Therefore, the linear function which models the data is f(x)
= 1.5x  3.
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