Question

The scatter plot below shows the relationship between the diameter (x), in mm, and mass f(x), in grams, of a berry: ordered pairs 11, 0.4 and 12, 0.8 and 13, 1.2 and 14, 1.6 and 15, 2 and 16, 2.4 and 17, 3 and 18, 3.2 and 19, 3.6 and 20, 4

Which of the following functions is best represented by the scatter plot?

f(x) = −0.4 + 4x

f(x) = 0.4 − 4x

f(x) = 4 − 0.4x

f(x) = −4 + 0.4x

Answer 1

For this case the first thing we must observe is that the mass increases 0.4 grams when the diameter increases 1 millimeter.
Therefore, the slope of the line is given by:
m = 0.4
Thus, the function that best suits the table is given by:
f (x) = -4 + 0.4x
For example, for x = 20 we have:
f (20) = -4 + 0.4 (20)
f (20) = -4 + 8
f (20) = 4
The result, matches the table.
Answer:
The function that is best represented by the scatter plot is:
f (x) = -4 + 0.4x