Question

Millie is cutting out stars to decorate the gym for the school dance. The number of stars (s) she can cut out varies directly with the time (t) in minutes she spends cutting out the stars. Look at the table below.

Time(t) in mintues Number of stars(s) s/t=k
0
12 6
15
44
50

Required:
a. Write an equation showing the relationship between s and t.
b. Complete the table to show the number of stars Millie is able to cut out for various amounts of time.
c. Write an equation to represent the relationship between s and t using the value of k you determined from the table.
d. Graph the data. Label x- and y-axis and title the graph
e. Did the graph turn out as you expected? Explain.
f. Explain how to determine the constant of proportionality using the graph.

Answer 1

The answer is below

Explanation:

a) the ratio of s to t is constant, that is s / t = constant

Since s / t = k. Therefore s = kt

From the table when s = 6, t = 12, hence:

6 / 12 = k

k = 0.5

s = kt = 0.5t

s = 0.5t

b)

Time (t) in minutes Number of stars (s) s/t = k

0

12 6 0.5

30 15 0.5

44 22 0.5

50 25 0.5

For s = 15: t = s / k = 15 / 0.5 = 30

For t = 44: s = kt = 44 * 0.5 = 22

For t = 50: s = kt = 50 * 0.5 = 25

c) for s = 6, t = 12

k = s / t = 6 / 12 = 0.5

s = kt = 0.5t

d) The graph is attached

e) The graph is a linear graph with a positive slope as expected

f) The equation can be gotten using the points (12, 6) and (25, 50) from the graph in the form (s, t):

`s-s_1=(s_2-s_1)/(t_2-t_1)(t-t_1)\\\\ s-6=(15-6)/(30-12)(t-12)\\\\s-6=0.5(t-12)\\\\s=0.5t-6+6\\\\s=0.5t \\\\`