Question

Nara got two new plants for her apartment. Each plant grew at a constant rate. The height (in centimeters) of the first plant as a function of time (in days since Nara got it) is given by the following table of values: \text{Time}Timestart text, T, i, m, e, end text (days) \text{Height}Heightstart text, H, e, i, g, h, t, end text (centimeters) 101010 343434 151515 363636 202020 383838 The graph of the height (in centimeters) of the second plant as a function of time (in days since Nara got it) is shown below. Which plant was taller when Nara got the plants?

Answer 1

Answer: They were equally tall, second plant.

Answer 2

They were equally tall

Explanation:

First plant

Time (days) Height (cm)

10 34

15 36

20 38

Using the first two points we can compute the slope (m) as follows:

m = (y2 - y1)/(x2 - x1) = (36 - 34)/(15 - 10) = 0.4

Using the first point and the slope, we can compute the y-intercept (b) as follows:

y1 = m*x1 + b

b = 34 - 0.4*10 = 30 cm

The graph of the height (in centimeters) of the second plant as a function of time (in days since Nara got it) is shown in the figure attached. We can see that its y-intercept is 30 cm.

In this context, y-intercept is the height of the plant when Nara got them.