A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table 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 that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)

Part A: There is a linear correlation between the number of hours of sunlight that a plant receives and the height it grows.

Part B: The function that best fits the data is

Part C: Slope indicates the height of the plant and y-intercept represents the initial height of the plant before receiving sunlight.

Explanation:

Part A: Let us determine it using the slope formula,

Let us substitute any two coordinates and

To find the y-intercept, the value of y-intercept is the value of y when the value of x is equal to zero.

Thus, y-intercept is 4 (b=4)

Let us substitute these values in the slope-intercept formula,

Thus, there is a linear correlation between the number of hours of sunlight that a plant receives and the height it grows.

Part B:

The function that best fits the data is given by

The explanation for the function is provided above.

Part C:

The slope is

This means that the height of the plant increases 3 centimeters  per hour of a sunlight received.

The y-intercept represents the initial height of the plant before receiving sunlight.

cheater

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4