Question

A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table below shows the data:


Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31


Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)

Part B: Write a function which best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)

Answer 1

Notice the x values `0 1 2 3 4 5 6 7 8 9` increase by 1 each time

at the same time, the y values `4 7 10 13 16 19 22 25 28 31` are increasing by what each time?

Answer 2

3

Answer 3

yes

these two facts will help us find the slope

slope = (change in y)/(change in x) = (+3)/(+1) = 3

slope = 3

Answer 4

ok so y= 3x+1?

Answer 5

the slope is m = 3
the y intercept is b = 4 this is the y value that corresponds to x = 0

Answer 6

now plug m = 3 and b = 4 into y = mx+b to get your linear equation

Answer 7

y= 3x+4

Answer 8

yes the last step you do is replace y with f(x) to get it into function notation form

Answer 9

that will wrap up part B

Answer 10

Is part A correct?

Answer 11

what did you write for part A?

Answer 12

There is a positive correlation between the number of hours of sunlight that a plant receives and the height to which it grows because as the hours increase, the plant grows taller.

Answer 13

yes that's correct

Answer 14

I also wrote Part C) That the plant starts at 4 cm which is the why intercept and increases by 3 cm each time which is the slope

Answer 15

Since a line fits through ALL of the points perfectly, we have a perfect correlation. Aka, a causation (one variable directly affects the other)

Answer 16

Y-intercept autocorrect oops

Answer 17

ok thank u

Answer 18

`That the plant starts at 4 cm` yes basically with no time in the sun, the plant is 4 cm tall

the slope of 3 means the plant increases 3 cm for each hour of sunlight

Answer 19

thank u!

Answer 20

no problem