For which values is the relationship linear? Tell how you decided. Write the equation for each linear relationship

x 5 10 15 20 25 30
y 20 30 40 50 50 50

I don't understand what the relationship has to do with being linear?

Does anyone know how to solve this.

In order to determine whether the relationship between x and y is linear, you need to examine how the values of y change as x increases. A linear relationship means that there is a constant rate of change between the two variables.

To check for a constant rate of change, you can calculate the difference between two consecutive values of y for each pair of consecutive values of x. If the differences between the y-values are consistent (i.e., the same for each pair of consecutive x-values), then the relationship is likely linear.

Let's calculate the differences for each pair of consecutive x-values:

For x = 5, the difference between y-values is 30 - 20 = 10.
For x = 10, the difference between y-values is 40 - 30 = 10.
For x = 15, the difference between y-values is 50 - 40 = 10.
For x = 20, the difference between y-values is 50 - 50 = 0.
For x = 25, the difference between y-values is 50 - 50 = 0.
For x = 30, there is no next value of x, so we cannot calculate the difference.

From these calculations, we can observe that the differences between y-values for the first three pairs of consecutive x-values (5-10, 10-15, 15-20) are all equal to 10. However, the differences between y-values for the last two pairs of consecutive x-values (20-25, 25-30) are both equal to 0.

Since the differences are not consistent, the relationship is not linear.

To write the equation for a linear relationship, assume the form y = mx + b, where m represents the slope and b represents the y-intercept. However, since the relationship given is not linear, we cannot write an equation for it in this form.