Question

Determine the initial value and the rate of change in the following description. A 2,000-gallon tank is half full with 1,000 gallons of water. Water is being pumped into the tank at a rate of 15 gallons per minute.(1 point) The initial value is b =, and the rate of change is m =

Answer 1

Use the table to answer the question. x is: 1, and -3. Y intercept is: 4, and 8. Find the rate of change and the initial value of the linear function given as a table of values. (1 point) The rate of change is m =, and the initial value is b =

Answer 2

I have given you the table. You can answer the question.

Answer 3

I already given you the table!!! The table goes like this: x is: 1, and -3. Y intercept is: 4, and 8.

Answer 4

That's wrong!

Answer 5

well, -1 is correct. But I said 4 is wrong!

Answer 6

The initial value, b, is 1,000 gallons (since the tank is initially half full with 1,000 gallons of water).
The rate of change, m, is 15 gallons per minute (since water is being pumped into the tank at a rate of 15 gallons per minute).

Answer 7

To find the rate of change (m) and the initial value (b) in a linear function given a table of values, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1)

Using the given values, we can find the rate of change at two points:

For x = 1 and y = 4:
m = (4 - b) / (1 - x)
m = (4 - b) / (1 - 1)
m = (4 - b) / 0

For x = -3 and y = 8:
m = (8 - b) / (-3 - x)
m = (8 - b) / (-3 - (-3))
m = (8 - b) / 0

Since division by zero is not defined, we cannot determine the rate of change from this table of values. The initial value (b) is also not provided.

Answer 8

Apologies for the confusion. If you have provided a table of values, please provide the values in the table for both x and y. Then, I will be able to calculate the rate of change (m) and the initial value (b).

Answer 9

Apologies for the misunderstanding.

Given the table:

x: 1, -3
y: 4, 8

To find the rate of change (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the table:

m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1

The rate of change is -1.

To find the initial value (b), we can use the y-intercept. The y-intercept represents the value of y when x is 0. In this case, the y-intercept is given as 4. Therefore, the initial value (b) is 4.

So, the rate of change (m) is -1 and the initial value (b) is 4.

Answer 10

Apologies for the incorrect response. Let's find the rate of change and the initial value based on the given table of values:

Given the table:

x: 1, -3
y: 4, 8

To find the rate of change (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the values from the table:

m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1

The rate of change is -1.

To find the initial value (b), we can use the y-intercept. The y-intercept represents the value of y when x is 0. In this case, the y-intercept is given as 4. Therefore, the initial value (b) is 4.

So, the rate of change (m) is -1 and the initial value (b) is 4.

Answer 11

Apologies for the mistake in my previous response.

Given the table:

x: 1, -3
y: 4, 8

To find the rate of change (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the values from the table:

m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1

The rate of change is -1.

To find the initial value (b), we can use the y-intercept. The y-intercept represents the value of y when x is 0. However, the table does not provide the value of y when x is 0, so we cannot determine the initial value based on the given table.

Apologies for the confusion and thank you for pointing that out.