The table shows how much a painter charges for painting a home. Is the relationship shown linear? Explain.
| hours worked | amount charged |
———————————————
| 1 | 35 |
| 2 | 50 |
| 3 | 70 |
| 4 | 90 |
———————————————
Idk where to start 😐
if it is linear it has a constant slope.
slope is ychange/xchange
Since all the x changes are the same, from step to step,
just check to see whether y always changes by the same amount. It does not.
So, not linear.
Now, if the first line were "1 30" then it would be linear.
To determine if the relationship shown in the table is linear, we need to check if there is a constant rate of change between the hours worked and the amount charged.
Let's calculate the rate of change between each pair of data points:
- Between the first and second data points: (50 - 35) / (2 - 1) = 15 / 1 = 15
- Between the second and third data points: (70 - 50) / (3 - 2) = 20 / 1 = 20
- Between the third and fourth data points: (90 - 70) / (4 - 3) = 20 / 1 = 20
Since the rate of change is not constant, the relationship shown in the table is not linear. In a linear relationship, the rate of change between any two points should be the same. Therefore, we can conclude that the relationship in the table is not linear.
To determine if the relationship shown is linear, we need to analyze the data and see if there is a consistent pattern or trend between the hours worked and the amount charged.
First, let's calculate the difference in the amount charged between consecutive hours worked:
Difference between 1st and 2nd row: 50 - 35 = 15
Difference between 2nd and 3rd row: 70 - 50 = 20
Difference between 3rd and 4th row: 90 - 70 = 20
From these differences, we can observe that there is not a constant difference between the amounts charged. In a linear relationship, the difference between consecutive data points would remain the same.
Therefore, based on the given data, the relationship between hours worked and the amount charged is not linear.