Question

The scatter plot below shows the relationship between the length (x) in meters and mass f(x) in kg of a marine animal

(1,1)(2,11)(3,21)(4,31)(5,41)(6,52)(7,65)(8,71)(9,82)(10,94)

Which of the following function is best represented by the scatter plot?
a. F(x)=9-10.3x
b. F(x)=-10.3+9x
c. F(x)=-9+10.3x
d. F(x)=10.3-9x

Answer 1

Option C.

Explanation:

As we can see from the graph, we have plotted the different points.

If the line drawn through the scatter plots, shows the relationship between the length x and mass f(x) then the function will be in the form of

f(x) = mx + b

where m = slope of the line that fits the best

b = y-intercept of the line

Since the plotted line passes through two pints (1, 1) and (10, 94).

Then the slope m =
`(y-y')/(x-x')`

m =
`((94-1))/(10-1)`

m =
`(93)/(9)`

m = 10.3

Now we place the coordinates (1, 1) in the equation to find the value of y-intercept b.

1 = 10.3 + b

b = 1 - 10.3

b = -9.3 ≈ 9

So the function will be f(x) = 10.3x - 9

Option C is the answer.