The graph shows the relationship between the time in minutes, x, and the number of gallons of water, y, being pumped into a pool.a. explain what each of the following coordinates means in terms of the time and the number of gallons of water: (0,0), (1,5), and (6,30). What is the unit rate? How do you know?

b. Write an equation that can be used to find the number of gallons of water, y, in the pool at any time, x. Identify the constant of proportionality in the equation.

Thank u!

Answers

Answer 1

Answer:

a. The coordinates (0, 0), (1, 5), and (6, 30) represent the initial state, the unit rate of 5 gallons per minute, and the cumulative gallons added, respectively.

b. The equation y = 5x represents the relationship, with the constant of proportionality being 5 (gallons per minute).

a. In the context of the graph showing the relationship between time (x in minutes) and the number of gallons of water (y), we can interpret the given coordinates as follows:

(0, 0): This point (0, 0) means that when there is no time (x = 0 minutes), no water has been pumped into the pool (y = 0 gallons). It represents the starting point before any water pumping began.

(1, 5): At (1, 5), it indicates that after 1 minute of pumping (x = 1 minute), 5 gallons of water (y = 5 gallons) have been added to the pool. This suggests that the unit rate of water pumping is 5 gallons per minute. We can determine the unit rate by examining how much the number of gallons (y) changes for each unit increase in time (x).

(6, 30): At (6, 30), it shows that after 6 minutes of pumping (x = 6 minutes), a total of 30 gallons of water (y = 30 gallons) have been pumped into the pool. The unit rate here is still 5 gallons per minute, as for every minute, 5 gallons are added.

b. To write an equation representing this relationship, we can express it as a linear equation in the form y = mx, where m represents the constant rate of change (the unit rate) which is 5 gallons per minute. So, the equation is:

y = 5x

In this equation, the constant of proportionality (m) is 5, as it represents the rate at which gallons of water are added per minute. This equation can be used to find the number of gallons of water (y) in the pool at any time (x) in minutes, given that the unit rate of pumping is 5 gallons per minute.

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Answer 2

Answer:

Answer:

The coordinate (0,0) means that in 0 minutes 0 gallons are pumped. (1,5) means that in one minute 5 gallons are pumped. (6,30) means that in 6 minutes 30 gallons are pumped. The unit rate is 5 because for each minute 5 gallons are pumped. The equation is y=5x. The constant of proportionality is 5.

Step-by-step explanation:

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an easy way to do it is subtituet (-7,5) and (-4,1) into the equations and find out which ones check. remember (x,y)

so A
if we try (-7,5)
5-7=-3/4(-7+5)
we can immediately see that -2 is not equal to -3/4(-2)
so A is wrong

B
if we try (-7,5)
5-5=-4/3(-7+7)
0=-4/3(0)
0=0
so B is correct

C
if we try (-7,5)
5+4=-3/4(-7+1)
9=-3/4(-6)
9 is not equal to 18/4
so C is wrong

D
if we try (-7,5)
5-1=-4/3(-7+4)
4=-4/3(-3)
4=12/3
4=4
D is correct

If you wanted to try the second point (-4,1) in B and D
B
1-5=-4/3(-4+7)
-4=-4/3(3)
-4=-12/3
4=4
B is still correct

D
1-1=-4/3(-4+4)
0=-4/3(0)
0=0
D is still correct

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Answers

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