Write a linear function that describes the earnings for each manager.
A
Manager B
B
More than 5 hours
Practice makes perfect
Consider that Manager A earns 15 dollars per hour and receives a 50 bonus. The earnings of Manager B are showed in the given graph.
We want to know which manager has greater hourly wage. To do so, let's find the slope of the line that represents the earnings of manager B. We will recall the slope formula.
m = y_2-y_1/x_2-x_1
We can substitute ( 3, 75) and ( 5, 125) into the above formula to obtain the slope.
Since x represents the working hours and y indicates the earnings, the slope means that the manager B earns 25 dollars per hour. Therefore, the manager B have a grater hourly wave.
Since the manager A receives 15 dollars per hour plus a 50 dollares bonus, we can describe their earnings by writing a linear function. To do so, consider that the earnings can be written as the product of 15 multiplied by the number of hours plus the bonus.
y_A=15x +50Here, x represents the worked hours. We can do the same for the earnings of manager B, but this time the earnings will be the product of 25 multiplied by the number of hours.
y_B=25x
We want to find after how many hours the manager B will earn more money than manager A. To find it, we can use an inequality where the earnings of manager B are greater than the earnings of manager A. We will solve the inequality for x to find the number of hours for which the the manager B earns more money. Let's do it!
