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 in this description is the entrance fee, which is $12 per person.
The rate of change is the cost for each additional ride. In this case, the rate of change is $2 per ride.
The initial value in this description is the amount of water in the tank, which is 1000 gallons.
The rate of change is the rate at which water is being pumped into the tank, which is 15 gallons per minute.
To find the rate of change and the initial value of the linear function given by the table of values, we can use the formula for the slope of a line.
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
Using the given points (1, 4) and (-3, 8), we can substitute the coordinates into the formula:
slope = (8 - 4) / (-3 - 1) = 4 / -4 = -1
Therefore, the rate of change of the linear function is -1.
To find the initial value of the linear function, we can choose one of the points and substitute it into the equation y = mx + b, where y is the output (dependent variable), x is the input (independent variable), m is the slope, and b is the initial value.
Let's choose the point (1, 4):
4 = -1 * 1 + b
4 = -1 + b
b = 4 + 1
b = 5
Therefore, the initial value of the linear function is 5.
In conclusion, the rate of change of the linear function is -1 and the initial value is 5.
determine the initial value and the rate of change in the following description. a 2,000 gallon tank is half full with 1000 gallons of water. Water is being pumped into the tank at a rate of 15 gallons per minute
x/y
1 4
-3 8
find the rate of change and the inital value of the linear function given as a table of values
(-3, 2.5)
(0,1)
(2,0)
determine the initial value and the rate of change of the lienar functon as given in the graph
To determine the initial value and rate of change of the linear function given by the graph, we can use any two points to calculate the slope. Let's use the points (-3, 2.5) and (0, 1).
The slope of a linear function can be calculated as:
slope = (change in y) / (change in x)
Using the points (-3, 2.5) and (0, 1):
slope = (1 - 2.5) / (0 - (-3))
= (-1.5) / (3)
= -0.5
Therefore, the rate of change of the linear function is -0.5.
To find the initial value, we can choose one of the points and substitute it into the equation y = mx + b, where y is the output (dependent variable), x is the input (independent variable), m is the slope, and b is the initial value.
Let's choose the point (0, 1):
1 = -0.5 * 0 + b
1 = b
Therefore, the initial value of the linear function is 1.
In conclusion, the rate of change of the linear function is -0.5 and the initial value is 1.