Height Above Canyon Floor Time (minutes)

360 0
280 3
160 10
80 14
Which statement best interprets the rate of change of the linear model shown in the table?
A. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute
B. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of -20 feet per minute
C. The elevation of a hiker who is hiking down a canyon floor changes at a rate of --20 feet per minute
D. The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute

9 answers

A. The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute

The table shows that as the height above the canyon floor decreases, the time increases. This indicates that the hiker is climbing up from the canyon floor, so the rate of change would be positive. The difference in height divided by the difference in time between each data point is 80 / 4 = 20 feet per minute.
Number of Months Cost ($)
1 74
2 99
3 124
4 149
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. $49
B. $25
C. $74
D. $37.25
D. $37.25

To find the slope, we need to calculate the change in cost divided by the change in number of months between two consecutive data points.

For example, between the first and second month:
Change in cost = 99 - 74 = 25
Change in number of months = 2 - 1 = 1
Slope = 25 / 1 = $25

Similarly, we can calculate the slope for the other data points:
- Between the second and third month: 124 - 99 = 25 (Change in cost), 3 - 2 = 1 (Change in number of months) => Slope = 25 / 1 = $25
- Between the third and fourth month: 149 - 124 = 25 (Change in cost), 4 - 3 = 1 (Change in number of months) => Slope = 25 / 1 = $25

Therefore, the monthly cost (slope) 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?
A. The parking fee rises by $7.33 with each additional hour
B. The parking fee rises by $6 with each additional hour
C. The parking fee rises by $8 with each additional hour
D. The parking fee rises by $10 with each additional hour
B. The parking fee rises by $6 with each additional hour

To find the rate of change (slope) of the graph, we calculate the change in fee divided by the change in hours between the two points given.

Using the points (2,20) and (6,44):
Change in fee = 44 - 20 = 24
Change in hours = 6 - 2 = 4
Slope = 24 / 4 = $6

Therefore, the interpreted slope represents that the parking fee rises by $6 with each additional hour.
(3,80) (1,160)
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?
A. -40 gal./hr
B. 40 gal./hr
C. -1/40 gal./hr
D. 1/40 gal./hr
B. 40 gal./hr

To find the rate of change (slope) between the two points (1,160) and (3,80), we again calculate the change in y (number of gallons) divided by the change in x (hours).

Using the points given:
Change in y = 80 - 160 = -80
Change in x = 3 - 1 = 2
Slope = -80 / 2 = -40 gallons per hour

Therefore, the rate of change in the number of gallons in the pool after each hour has passed is -40 gal./hr.
Which formula can be used to find the slope of a line from two points (x1,y1) and (x2,y2) ?
A. y2/y1 - x2/x1
B. y2 - y1/x2 - x1
C. y2+ y1/ x2+x1
D. x2-x1/y2-y1
B. y2 - y1/x2 - x1

The formula to find the slope of a line passing through two points (x1, y1) and (x2, y2) is:

Slope = (y2 - y1) / (x2 - x1)