Question

Part B

1. Which of the following lines of best fit represent the data if x is the number of days since the plant appeared and y is the height of the plant?
A. y = –3.5x + 0.7 wrong
B. y = –0.7x + 3.5 wrong
C. y = 0.7x + 3.5 wrong
D. y = 3.5x + 0.7 correct


2. Explain why your choice of equations best fits the data. Explain what the slope and y-intercept of the line of best fit mean about the bamboo plants.







Part C
Use the line of best fit chosen in part B to predict the height of a bamboo plant 40 days after appearing above the soil. Show your work.

Answer 1

a) Correct: D

b) Plants grow 3.5 units of height each day

c) 140.7 units

Explanation:

Looking at the graph we can see the relation between x and y is an increasing function, which means when x increases, y also does

a) The alternative D is the correct one

b) Increasing lines have a positive slope and the slope is the coefficient of x. The first two alternatives (A and B) have negative slopes, so they are discarded.

To decide between C or D, we see that when x is near 30, y is near 110 and the y-intercept is close to zero. The division of 110/30 = 3.67 must be near the slope of the correct line.

So the alternative D is the correct one

The slope means how fast the bamboo plants grow in time. It can be understood that they grow 3.5 units of height each day.

The y-intercept is interpreted as the initial height of the bamboo plants at day zero (assuming the experiment was conducted after it appeared above the soil)

c) If we use the relation

y=3.5x+0.7 and set x=40 days, we have

y=(3.5)(40)+0.7 = 140.7 units of height