Determine the initial value and the rate of change in the following description. At a local festival, the entrance fee is $12 per person, and ride tickets cost $2 for every ride.

Question

The initial value is b =__, and the rate of change is m = __.

Answer 1

The initial value, b, is $12 per person for the entrance fee.

The rate of change, m, is $2 for every ride ticket.

Answer 2

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.
The initial value is b = __, and the rate of change is m = __.

Answer 3

The initial value, b, is 1,000 gallons, which is the amount of water in the tank initially when it is half full.

The rate of change, m, is 15 gallons per minute, which is the rate at which water is being pumped into the tank.

Answer 4

x 1, -3
y 4, 8
Find the rate of change and the initial value of the linear function given as a table of values.
The rate of change is m = __, and the initial value is b = __.

Answer 5

To find the rate of change, we use the formula:
m = (change in y) / (change in x)

Given the points:
Point 1: (x1, y1) = (1, 4)
Point 2: (x2, y2) = (-3, 8)

Change in y = y2 - y1 = 8 - 4 = 4
Change in x = x2 - x1 = -3 - 1 = -4

Therefore, the rate of change is:
m = 4 / (-4) = -1

To find the initial value, we can use the point-slope form of a linear function:
y = mx + b

Using the first point (1, 4):
4 = -1(1) + b
4 = -1 + b
b = 5

Therefore, the initial value is b = 5.

Answer 6

(0,0) (2,3)
Determine the initial value and the rate of change of the linear function given in the graph.
The initial value is __, and the rate of change is __.

Answer 7

To determine the initial value and rate of change of the linear function given the points (0,0) and (2,3), we can follow a similar process as before.

The rate of change, m, is given by the formula:
m = (change in y) / (change in x)

Using the given points:
Point 1: (x1, y1) = (0, 0)
Point 2: (x2, y2) = (2, 3)

Change in y = y2 - y1 = 3 - 0 = 3
Change in x = x2 - x1 = 2 - 0 = 2

Therefore, the rate of change is:
m = 3 / 2 = 1.5

To find the initial value, we can use the point-slope form of a linear function:
y = mx + b

Using the point (0,0):
0 = 1.5(0) + b
0 = 0 + b
b = 0

Therefore, the initial value is b = 0, and the rate of change is m = 1.5.

Answer 8

(2,0) (0,1) (-3,2.5)
Determine the initial value and the rate of change of the linear function as given in the graph.
The initial value is __, and the rate of change is __.

Answer 9

To determine the initial value and rate of change of the linear function given the points (2,0), (0,1), and (-3,2.5), we can follow a similar process as before.

The rate of change, m, is given by the formula:
m = (change in y) / (change in x)

Using the given points:
Point 1: (x1, y1) = (2, 0)
Point 2: (x2, y2) = (0, 1)
Point 3: (x3, y3) = (-3, 2.5)

Change in y for the first set of points = -1
Change in x for the first set of points = -2
Change in y for the second set of points = 2.5 - 1 = 1.5
Change in x for the second set of points = -3 - 0 = -3

Therefore, the rate of change is the average of these two sets:
Rate of change = (-1 - 1.5) / (-2 + (-3)) = -2.5 / -5 = 0.5

To find the initial value, we can use the point-slope form of a linear function:
y = mx + b

Using any of the given points (e.g., (0,1)):
1 = 0.5(0) + b
1 = 0 + b
b = 1

Therefore, the initial value is b = 1, and the rate of change is m = 0.5.

Answer 10

its not 0.5

Answer 11

I apologize for the error in my previous response. Let's reevaluate the rate of change using the points provided.

Given points:
Point 1: (2, 0)
Point 2: (0, 1)
Point 3: (-3, 2.5)

Rate of change, m:
For the first set of points:
Change in y = 0 - 1 = -1
Change in x = 2 - 0 = 2
Rate of change for the first set of points: m1 = -1 / 2 = -0.5

For the second set of points:
Change in y = 1 - 2.5 = -1.5
Change in x = 0 - (-3) = 3
Rate of change for the first set of points: m2 = -1.5 / 3 = -0.5

The rate of change for both sets of points is the same, -0.5.

To find the initial value, we can use any of the given points in the linear function equation y = mx + b. Let's use (2, 0):
0 = -0.5(2) + b
0 = -1 + b
b = 1

Therefore, the initial value is b = 1, and the rate of change is m = -0.5. Thank you for pointing out the error.