X=Height Above Canyon Floor Y=Time (minutes)
X360 Y0
X280 Y3
X160 Y10
X80 Y14
Which statement best interprets the rate of change of the linear model shown in the table?
1. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
2. The elevation of a hiker who is hiking up from canyon floor changes at a rate of , negative 20, feet per minute.
3. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
4. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.
2. The elevation of a hiker who is hiking up from the canyon floor changes at a rate of negative 20 feet per minute.
Number of Months Cost ($)
1m = $74
2m = $99
3m = $124
4m = $149
The table below shows the cost for a gym membership at the local fitness center with an initial start-up fee charged in the first month. Find the slope, or monthly cost.
A. $37.25
B. $49
C. $25
D. $74
The slope represents the rate of change of the cost per month. We can use the formula for slope:
slope = (change in y)/(change in x)
In this case, y is the cost and x is the number of months. Let's choose two points from the table to calculate the slope. We can choose (1, 74) and (2, 99):
slope = (99-74)/(2-1) = 25
Therefore, the slope or monthly cost for the gym membership is $25. Answer: C. $25.
To determine the rate of change from the given table, we need to look at the change in the dependent variable (elevation) over the change in the independent variable (time). In this case, the independent variable is the time (Y) and the dependent variable is the height above the canyon floor (X).
First, let's calculate the change in elevation between two consecutive data points:
- From (X360, Y0) to (X280, Y3), the change in elevation is 0 - 3 = -3
- From (X280, Y3) to (X160, Y10), the change in elevation is 3 - 10 = -7
- From (X160, Y10) to (X80, Y14), the change in elevation is 10 - 14 = -4
Next, let's calculate the change in time between two consecutive data points:
- From (X360, Y0) to (X280, Y3), the change in time is 0 - 3 = -3
- From (X280, Y3) to (X160, Y10), the change in time is 3 - 10 = -7
- From (X160, Y10) to (X80, Y14), the change in time is 10 - 14 = -4
Now, we can find the rate of change by dividing the change in elevation by the change in time:
- From (X360, Y0) to (X280, Y3), the rate of change is -3 / -3 = 1 feet per minute
- From (X280, Y3) to (X160, Y10), the rate of change is -7 / -7 = 1 feet per minute
- From (X160, Y10) to (X80, Y14), the rate of change is -4 / -4 = 1 feet per minute
Since the rate of change is consistently 1 feet per minute, the correct statement is:
1. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
(Note: The feet per minute is positive because it represents an upward change in elevation)