Use the table to answer the question.
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 down to a canyon floor changes at a rate of −20 feet per minute.
B. The elevation of a hiker who is hiking up from canyon floor changes at a rate of −20 feet per minute.
C. The elevation of a hiker who is hiking up from 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 down to a canyon floor changes at a rate of −20 feet per minute.
Use the table to answer the question.
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. $37.25
B. $49
C. $25
D. $74
Number of Months Cost ($)
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. $37.25
B. $49
C. $25
D. $74
To find the slope, we need to determine the change in cost over the change in number of months.
The change in cost over the change in number of months for the given data points can be calculated using the formula:
Slope = (Cost at month 2 - Cost at month 1) / (Number of months at month 2 - Number of months at month 1)
Slope = (99 - 74) / (2 - 1)
Slope = 25
Therefore, the slope, or monthly cost, is $25.
Therefore, the answer is C. $25.
The change in cost over the change in number of months for the given data points can be calculated using the formula:
Slope = (Cost at month 2 - Cost at month 1) / (Number of months at month 2 - Number of months at month 1)
Slope = (99 - 74) / (2 - 1)
Slope = 25
Therefore, the slope, or monthly cost, is $25.
Therefore, the answer is C. $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 $8 with each additional hour.
B. The parking fee rises by $6 with each additional hour.
C. The parking fee rises by $10 with each additional hour.
D. The parking fee rises by $7.33 with each additional hour.
A. The parking fee rises by $8 with each additional hour.
B. The parking fee rises by $6 with each additional hour.
C. The parking fee rises by $10 with each additional hour.
D. The parking fee rises by $7.33 with each additional hour.
To calculate the rate of change, we first need to find the slope of the line passing through the points (2,20) and (6,44).
The formula for slope is:
Slope = (change in y) / (change in x)
Slope = (44 - 20) / (6 - 2)
Slope = 24 / 4
Slope = 6
Therefore, the slope of the graph represents the rate of change in the parking fee for each additional hour of parking. In this case, the parking fee rises by $6 with each additional hour.
So, the correct answer is:
B. The parking fee rises by $6 with each additional hour.
The formula for slope is:
Slope = (change in y) / (change in x)
Slope = (44 - 20) / (6 - 2)
Slope = 24 / 4
Slope = 6
Therefore, the slope of the graph represents the rate of change in the parking fee for each additional hour of parking. In this case, the parking fee rises by $6 with each additional hour.
So, the correct answer is:
B. The parking fee rises by $6 with each additional hour.
Use the image to answer the question.
A coordinate plane shows the x-axis, labeled as hours, ranging from 0 to 6 in increments of 1 and the y-axis, labeled as gallons, ranging from 0 to 240 in increments of 20. A line segment joins four plotted points. The coordinates of the plotted points are left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 160 right parenthesis, left parenthesis 3 comma 80 right parenthesis, and left parenthesis 5 comma 0 right parenthesis.
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. 140 gal./hr.
C. 40 gal./hr.
D. −140 gal./hr.
A coordinate plane shows the x-axis, labeled as hours, ranging from 0 to 6 in increments of 1 and the y-axis, labeled as gallons, ranging from 0 to 240 in increments of 20. A line segment joins four plotted points. The coordinates of the plotted points are left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 160 right parenthesis, left parenthesis 3 comma 80 right parenthesis, and left parenthesis 5 comma 0 right parenthesis.
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. 140 gal./hr.
C. 40 gal./hr.
D. −140 gal./hr.
To find the rate of change in the number of gallons in the pool after each hour has passed, we can use the formula for slope:
Slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Using the given points (1, 160) and (3, 80):
Slope = (80 - 160) / (3 - 1) = -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.
So, the correct answer is:
A. -40 gal./hr.
Slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Using the given points (1, 160) and (3, 80):
Slope = (80 - 160) / (3 - 1) = -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.
So, the correct answer is:
A. -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−y1x2−x1
B. y2y1−x2x1
C. x2−x1y2−y1
D. y2+y1x2+x1
A. y2−y1x2−x1
B. y2y1−x2x1
C. x2−x1y2−y1
D. y2+y1x2+x1
The formula to find the slope of a line from two points (x1, y1) and (x2, y2) is:
Slope = (y2 - y1) / (x2 - x1)
So, the correct formula is:
A. y2−y1 / x2−x1
Slope = (y2 - y1) / (x2 - x1)
So, the correct formula is:
A. y2−y1 / x2−x1
1 answer