Write an equation that shows the relationship between the quantities; the total cost of hiring a certain plumber is a flat rate of $35 plus $9.50/hr.

C = 35 + 9.5 T

T is the number of hours worked. C is the total cost.

To write an equation that shows the relationship between the quantities, we need to define the variables involved. Let's use the following variables:

C = total cost of hiring the plumber
h = number of hours of work

Based on the given information, we know that there is a flat rate of $35 and an additional hourly rate of $9.50. The equation for the total cost can be written as:

C = 35 + 9.50h

In this equation, the $35 represents the flat rate and the 9.50h represents the hourly rate (9.50 multiplied by the number of hours of work, h). By substituting different values for h, you can find the total cost for hiring the plumber for a given number of hours.