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?

Answer 1

The function would be f (x) = 0.4x - 4.

Explanation
We can see that this is linear, since it increases at a constant rate.  We find the slope using the formula
m=(y₂-y₁)/(x₂-x₁) = (0.8-0.4)/(12-11) = 0.4/1 = 0.4

We use point-slope form to write the initial equation:

y-y₁ = m(x-x₁)
y-0.4 = 0.4(x-11)

Using the distributive property:
y-0.4 = 0.4*x - 0.4*11
y-0.4 = 0.4x-4.4

Add 0.4 to both sides:
y-0.4+0.4 = 0.4x-4.4+0.4
y=0.4x-4