The table shows how much a painter charges for painting a home. Is the relationship shown linear?
Explain.
Hours worked is the left side and Amount Charged is the right side.
1| 35
2| 50
3| 70
4| 90
I'm not understanding what to do first
graph charges vs hours. Is it a line?
Now to examine it with your mind, look at the gap between 1 and 2 hours. The change of one hour (1 to 2) is 15 dollars (from 35 to 5o). Now look at the gap between 3,4: a change of one hour is 20 dollars. and from 2 to 3, one hour increase is 20 dollars.
so here are the slopes
So it appears at first glance, that the "service call" is 5 dollars, then the rate per hour is 20. PLOT IT.
The ratios should be equal if linear:
35/1 = ?
50/2 = ?
70 /3 = ?
90/4 = ?.
To determine if the relationship shown in the table is linear, we need to examine the pattern between the hours worked and the amount charged.
One way to approach this is to calculate the difference in amounts charged for consecutive hours worked. Let's calculate the differences:
2 - 1 = 15
3 - 2 = 20
4 - 3 = 20
As we can see, the differences between consecutive hours worked are not consistent. In a linear relationship, the differences would be the same or have a constant pattern. However, in this case, the differences are not equal, indicating that the relationship is not linear.
Another way to determine if the relationship is linear is to plot the data points on a graph. By graphing the points, we can visually see if there is a straight line pattern.
Let's plot the points on a graph:
- Place the hours worked on the x-axis.
- Place the amount charged on the y-axis.
Plotting the points (1, 35), (2, 50), (3, 70), and (4, 90) on the graph, we can see that they do not fall on a straight line. The points form a curve, indicating that the relationship is not linear.
In conclusion, based on both the calculations and graph, we can determine that the relationship shown in the table is not linear.