(2,10) (3,15) (6,30)
The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.
To find the unit rate, we need to determine the stretch of the spring per gram of weight.
Given that the stretches of the spring are 10mm, 15mm, and 30mm for weights of 2g, 3g, and 6g respectively, we can divide the stretch of the spring by the weight to find the unit rate.
For the first data point, the unit rate is 10mm / 2g = 5mm/g.
For the second data point, the unit rate is 15mm / 3g = 5mm/g.
For the third data point, the unit rate is 30mm / 6g = 5mm/g.
Therefore, the unit rate is 5mm/g.
(2,14) (3,21) (4,28)
Using the points shown in the graph, identify the constant of proportionality for this graph.
To find the constant of proportionality for this graph, we can choose any two points and divide the change in the dependent variable (y-value) by the change in the independent variable (x-value).
Let's choose the first two points (2, 14) and (3, 21) to calculate the constant of proportionality.
The change in the dependent variable is 21 - 14 = 7.
The change in the independent variable is 3 - 2 = 1.
Dividing the change in the dependent variable by the change in the independent variable gives us:
7 / 1 = 7.
Therefore, the constant of proportionality for this graph is 7.
(1,3) (0.5, 4.5) (1,6) (7.5, 1.5)
Identify the distance a sloth travels per minute.
To find the distance a sloth travels per minute, we need to determine the change in the distance (dependent variable) divided by the change in time (independent variable) for any two points.
Let's calculate the distance traveled per minute using the first two points, (1, 3) and (0.5, 4.5).
The change in distance is 4.5 - 3 = 1.5.
The change in time is 0.5 - 1 = -0.5.
Dividing the change in distance by the change in time gives us:
1.5 / -0.5 = -3.
Therefore, the sloth is traveling at a rate of -3 units of distance per minute.
However, since the distance traveled cannot be negative in this context, we can take the absolute value of the rate. Therefore, the sloth is traveling at a rate of 3 units of distance per minute.
(2,2) (0,2) (2,3) (4,4) (2,5) (7,7) (4,7) (5,8) (4,8)
Three friends are playing video games. The graph shows the number of levels passed based on amount of time played. Which friend’s graph (1, 2, or 3) is a proportional relationship?
To determine which friend's graph represents a proportional relationship, we need to check if the ratios between the number of levels passed and the amount of time played stay constant.
Let's check the ratios for each friend:
Friend 1: (2,2), (4,4), (7,7)
Ratio between levels passed and time played: 2/2 = 1, 4/4 = 1, 7/7 = 1
Friend 2: (0,2), (2,3), (5,8)
Ratio between levels passed and time played: 2/2 = 1, 3/2 = 1.5, 8/5 = 1.6
Friend 3: (2,3), (4,7), (4,8)
Ratio between levels passed and time played: 3/2 = 1.5, 7/4 = 1.75, 8/4 = 2
From the ratios calculated, we can see that only Friend 1 has a constant ratio of 1 for all their data points. Therefore, Friend 1's graph represents a proportional relationship.