Final answer:
To earn $450, Sam must work 7 hours.
Step-by-step explanation:
In this question, the independent variable is the number of hours Sam works to perform the repair, and the dependent variable is the amount of money he earns. The equation that expresses the total amount of money Sam earns is y = 135 + 45x, where y represents the total amount of money and x represents the number of hours of service. The y-intercept of the equation is 135, which means that Sam charges $135 for a service call. The slope of the equation is 45, which means that Sam charges an additional $45 per hour of service.
To earn $450, we need to solve the equation 450 = 135 + 45x for x. Subtracting 135 from both sides of the equation gives us 450 - 135 = 45x. Simplifying gives us 315 = 45x. Dividing both sides of the equation by 45 gives us x = 7. Therefore, Sam must work 7 hours to earn $450.