In the table, x represents every mile driven in a cab and y represents the cost.
A 2-column table with 5 rows. Column 1 is labeled x with entries 1.25, 2.50, 3.75, 5, 6.25. Column 2 is labeled y with entries 7.50, 10.0, 12.5, 15.0, 17.5.
Is the slope increasing or decreasing?
What is the slope for this scenario?
The slope is increasing because as x increases, y also increases.
The slope can be calculated using the formula:
slope = (change in y) / (change in x)
Using values from the table:
slope = (17.5 - 7.5) / (6.25 - 1.25)
slope = 10 / 5
slope = 2
Therefore, the slope for this scenario is 2.
To determine if the slope is increasing or decreasing, we can examine the rate at which the y-values change with respect to the x-values.
Given the data in the table, let's calculate the difference in y-values and x-values between consecutive rows:
For the first row to the second row:
Change in y-values = 10.0 - 7.50 = 2.50
Change in x-values = 2.50 - 1.25 = 1.25
For the second row to the third row:
Change in y-values = 12.5 - 10.0 = 2.50
Change in x-values = 3.75 - 2.50 = 1.25
For the third row to the fourth row:
Change in y-values = 15.0 - 12.5 = 2.50
Change in x-values = 5 - 3.75 = 1.25
For the fourth row to the fifth row:
Change in y-values = 17.5 - 15.0 = 2.50
Change in x-values = 6.25 - 5 = 1.25
As we can see, the change in y-values is the same (2.50) for each consecutive pair of rows, and the change in x-values is also the same (1.25). This means that for this scenario, the slope is constant and not changing. Therefore, the slope is neither increasing nor decreasing.
Now, let's calculate the slope:
The slope (m) can be calculated using the formula:
m = (change in y-values) / (change in x-values)
Using any consecutive rows, we can see that the change in y-values is always 2.50 and the change in x-values is always 1.25.
Therefore, the slope for this scenario is:
m = (2.50) / (1.25) = 2
So, the slope for this scenario is 2.