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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.
The initial value is b = __, and the rate of change is m = __.
The initial value is the entrance fee, which is $12 per person. Therefore, the initial value is b = $12.
The rate of change is the cost of each additional ride ticket, which is $2 per ride. Therefore, the rate of change is m = $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 the amount of water in the tank at the beginning, which is 1,000 gallons. Therefore, the initial value is b = 1,000 gallons.
The rate of change is the rate at which water is being pumped into the tank, which is 15 gallons per minute. Therefore, the rate of change is m = 15 gallons/minute.
Use the table to answer the question.
x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.
To find the rate of change and the initial value of the linear function given in the table, we first need to choose two points from the table to calculate the rate of change.
Let's choose the points (1, 4) and (-3, 8) from the table.
Rate of change (m) = (change in y) / (change in x)
m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1
Therefore, the rate of change of the linear function is -1.
Next, we can find the initial value (b) by substituting one of the points into the equation of a line. Let's use the point (1, 4).
Using the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) = (1, 4) and m = -1
y - 4 = -1(x - 1)
y - 4 = -x + 1
y = -x + 5
The initial value of the linear function is 5.