Question

Two lawn-mowing services are compared. The monthly cost, y dollars, as compared to the number of times the yard is mowed, x. The monthly cost of Service a is represented by y = 30x+20. The graph of service b costs goes through (0,0) and (5,150). how do these two services differ?

Answer 1

Service a charges $30 per mow plus an additional $20 flat fee each month, however, Service b only charges $30 per mow, so Service b would be cheaper.

Explanation:

This question is asking you to compare costs using linear equations. In a linear equation, 'x' represents the independent variable, in this case the number of times the yard is mowed, and 'y' represents the dependent variable, or the monthly cost. 30 is the slope, or rate of change, which in this problem is the cost per time the yard is mowed. In the equation for Service a, we can see that it is a charge of $30 per time, however, there is also an additional fee of $20 - which is our y-intercept. However, Service b has two points (0,0) and (5,150). Using these two points, we can find the slope, or rate, by subtracting the 'y' values over the 'x' values, or (150-0)/(5-0), to get 30. Since Service b has the starting point of (0,0), or cost is $0 when there are 0 lawns mowed, then they do not have a flat fee.