Height Above Canyon Floor
360
280
160
80
Time (minutes)
0
3
10
14
Which statement best interprets the rate of change of the linear model shown in the table?
statements:
The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking up from canyon floor changes at a rate of −20 feet per minute.
The statement that best interprets the rate of change of the linear model shown in the table is: The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
Number of Months
1
2
3
4
Cost ($)
74
99
124
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.
To find the slope, or monthly cost, we need to find the change in cost per change in number of months.
Using the formula for finding slope:
slope = (change in y) / (change in x)
In this case, the change in y is the change in cost, and the change in x is the change in number of months.
Taking any two points from the table, we can calculate the slope:
(1, 74) and (2, 99)
change in y = 99 - 74 = 25
change in x = 2 - 1 = 1
slope = 25 / 1 = 25
Therefore, the slope, or monthly cost, is $25.
A linear graph of parking fees in dollars based on hours parked has the points (2,20) and (6,44) . How would you interpret the slope of the graph as the rate of change in the parking fee for each additional hour of parking?
The parking fee rises by $10 with each additional hour.
The parking fee rises by $6 with each additional hour.
The parking fee rises by $8 with each additional hour.
The parking fee rises by $7.33 with each additional hour.
To interpret the slope of the graph as the rate of change in the parking fee for each additional hour of parking, we need to find the change in the fee per change in the number of hours.
Given the points (2,20) and (6,44), we can calculate the slope using the formula:
slope = (change in y) / (change in x)
(change in y) = 44 - 20 = 24
(change in x) = 6 - 2 = 4
slope = 24 / 4 = 6
Therefore, the slope of the graph is 6, and this means that the parking fee rises by $6 with each additional hour of parking.
The graph shows the number of gallons in a wading pool that is being drained. Using the points (1,160) and (3,80) as (x1,y1) and (x2,y2) , what is the rate of change in the number of gallons in the pool after each hour has passed?
−1/40 gal./hr.
1/40 gal./hr.
−40 gal./hr.
40 gal./hr.
To find the rate of change in the number of gallons in the pool after each hour has passed, we need to find the slope of the graph using the given points (1,160) and (3,80).
Using the slope formula:
slope = (change in y) / (change in x)
(change in y) = 80 - 160 = -80
(change in x) = 3 - 1 = 2
slope = -80 / 2 = -40
Therefore, the rate of change in the number of gallons in the pool after each hour has passed is -40 gal./hr.
what formula can be used to find the slope of a line from two points (x1,y1) and (x2,y2)
The formula to find the slope (m) of a line given two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
To interpret the rate of change of the linear model shown in the table, we need to look at how the height above the canyon floor changes over time.
Looking at the table, we can see that as the time increases, the height above the canyon floor decreases. This indicates that the hiker is descending down to the canyon floor.
The change in height is given as:
From 360 to 280: a change of -80 feet over 3 minutes.
From 280 to 160: a change of -120 feet over 7 minutes.
From 160 to 80: a change of -80 feet over 4 minutes.
So, the average rate of change is -80 feet per 3 minutes, or approximately -26.67 feet per minute.
Therefore, the statement that best interprets the rate of change of the linear model is:
"The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute."