An electrician charges a $50 fee to make a service call plus $25 per hour he works. Determine whether the relationship between the two variables is proportional.
Hours Cost($)
1 75
2 100
3 125
4 150
Is this proportional? Because i am not sure. When i plot these points on a graph, they don't pass the origin, which makes it not proportional. But these fractions are proportional otherwise, so is the answer proportional or not?
Kaitlyn, Jack, anonymous, hiii, anonnnn, anon, Shirley -- or whoever -- you've changed names again! Both Damon and I asked you to keep the same name for your posts.
If the line does not pass through the origin, it it not proportional.
you clearly have
y = 25x + 50
That "+ 50" wrecks the proportionality.
To determine whether the relationship between the two variables is proportional, we can check if the ratio between the two variables remains constant.
Let's calculate the ratio between hours and cost for each data point:
For 1 hour, the cost is $75: 75/1 = 75
For 2 hours, the cost is $100: 100/2 = 50
For 3 hours, the cost is $125: 125/3 ≈ 41.67
For 4 hours, the cost is $150: 150/4 = 37.5
Since the ratios are not the same for all data points, the relationship between hours and cost is not proportional.
Although the fractions may seem proportional, it's important to consider the definition of proportionality, which requires that the ratio between the two variables remains constant. However, in this case, as the number of hours increases, the ratio between hours and cost decreases.
Therefore, the relationship between hours and cost is not proportional.
To determine whether the relationship between the number of hours and cost in this scenario is proportional, we can examine the given data points.
If the relationship is proportional, it means that the ratio of cost to hours should be consistent for all data points.
Let's calculate the ratio (cost/hours) for each data point:
For the first data point (1 hour, $75):
Ratio = 75 / 1 = 75
For the second data point (2 hours, $100):
Ratio = 100 / 2 = 50
For the third data point (3 hours, $125):
Ratio = 125 / 3 ≈ 41.67
For the fourth data point (4 hours, $150):
Ratio = 150 / 4 = 37.5
As you can see, the ratio is not consistent for all data points. In a proportional relationship, the ratio would be the same for every point.
Therefore, we can conclude that the relationship between the number of hours and cost in this scenario is not proportional.
It is worth noting that although the relationship is not proportional, it can still have a consistent pattern. In this case, the cost increases by $25 for each additional hour worked, which is a linear relationship.