Question

The scatter plot below shows the relationship between the leaf length (x) and leaf width f(x), in mm, of some leaves of a tree:

ordered pairs 11, 0.5 and 12, 1 and 13, 1.5 and 14, 2 and 15, 2.5 and 16, 3 and 17, 3.5 and 18, 4 and 19, 4.5 and 20, 5 and 21, 5.5 and 22, 6

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

f(x) = −5 + 0.5x
f(x) = 5 + 0.5x
f(x) = x − 10.5
f(x) = −x − 10.5

Answer 1

f(x)=-5+0.5x

sryy its late

Answer 2

The correct answer is f(x)=-5+0.5x

Looking at the data, we can see that the data increases at a constant rate. We can find this rate, the slope, using the formula
m=(y₂-y₁)/(x₂-x₁)

Using the first two ordered pairs, we have
m=(1-0.5)/(12-11) = 0.5/1 = 0.5

Writing this in point-slope form, y-y₁=m(x-x₁), we have
y-0.5=0.5(x-11)

Using the distributive property, we have
y-0.5=0.5x-0.5*11
y-0.5=0.5x-5.5

Adding 0.5 to both sides,
y-0.5+0.5=0.5x-5.5+0.5
y=0.5x-5