Question

Apolline is mowing lawns for a summer job. for every mowing job, she charges an initial fee plus a constant fee for each hour of work. her fee for a \[5\]-hour job, for instance, is \[\$42\]. her fee for a \[3\]-hour job is \[\$28\]. let \[y\] represent apolline's fee (in dollars) for a single job that took \[x\] hours for her to complete.

Answer 1

The equation that expresses Apolline's fee for a mowing job in terms of the number of hours it takes to complete is y = 7x + 7.

Step-by-step explanation:

The given problem involves finding a linear equation that expresses the total fee for a mowing job in terms of the number of hours it takes to complete. Let x represent the number of hours and y represent the fee. We are given two data points: for a 5-hour job, the fee is $42, and for a 3-hour job, the fee is $28. To find the equation, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

First, we can find the slope by finding the change in y divided by the change in x: m = (42-28)/(5-3) = 7. Next, we can substitute one of the data points into the equation and solve for b. Let's use the point (5, 42): 42 = 7(5) + b => b = 7. Therefore, the equation that expresses Apolline's fee for a single job that took x hours to complete is y = 7x +7.