Question

The table shows the linear relationship in a tank and time.

what is the rate of the change of water level feet per hour? also explain how

Answer 1

`y = mx + b`

y = slope (x) + y - intercept

To find the slope we need to find out how much the x's and y's increase or decrease...

To find the y - intercept if any, simply​ look for coordinates ( 0 , y ) or 0 and a #.

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In this case, as time passes, the water level decreases therefore we have a negative slope.

Time is our x and amount (ft) is our y.

On the x side it increases by 2

On the y side it decreases by 10

Now do y over x ==> 10 over 2 and get 5 ==> m

-5 is our slope and 50 is our y - intercept

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The "rate of change" is another word for slope.

Well, slope is - 5ft is our slope.


`y = - 5x + 50`

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Answer 2

The rate of change of the water level is 5 feet per hour, indicating a linear decrease. This is found by calculating the average rate of change using the given initial and final water levels and time.

To find the rate of change of the water level in feet per hour, we can use the formula for the average rate of change:

`\[ \text{Rate of change} = \frac{\text{Change in water level}}{\text{Change in time}} \]`

Given the table:

Change in water level = 50 ft - 20 ft = 30 ft

Change in time = 6 hr - 0 hr = 6 hr

Now, plug these values into the formula:

Rate of change =
`\frac{30 \, \text{ft}}{6 \, \text{hr}} = 5 \, \text{ft/hr}`

Therefore, the rate of change of the water level is 5 feet per hour. This indicates that the water level is decreasing by 5 feet every hour over the given time interval.