Janis was offered two different jobs when she graduated from college. She made the graph and table to show how much she would earn over time at each job. Earnings over Time for Job 1 Earnings over Time for Job 2. When will Janis’s salary be the same for job 1 and job 2, and how much will she be earning at that point? The salaries will be the same in year 20, and she will be earning $80,000. The salaries will be the same in year 16, and she will be earning $70,000. The salaries will be the same in year 12, and she will be earning $60,000. The salaries will be the same in year 10, and she will be earning $55,000.
Accepted Solution
A:
The salaries will be the same in year 20 and she will be earning $80,000.
We first create an equation to represent the data in the table. To find the slope we use the formula m = (y₂-y₁)/(x₂-x₁) = (60,000-55,000)/(12-10) = 5,000/2 = 2500
Writing this in point-slope form, we have y-y₁=m(x-x₁) y-55,000 = 2500(x-10)
Converting to slope-intercept form, we first use the distributive property: y-55,000 = 2500*x - 2500*10 y-55,000 = 2500x - 25,000
Adding 55,000 to both sides, y = 2500x+30,000
Now we set this equal to the equation from the graph: 2500x+30,000 = 2000x+40,000
Subtract 2000x from both sides: 2500x+30,000-2000x = 2000x+40,000-2000x 500x+30,000 = 40,000
Subtract 30,000 from both sides: 500x+30,000-30,000 = 40,000-30,000 500x = 10,000
Divide both sides by 500: 500x/500 = 10,000/500 x = 20
The salaries will be the same in year 20. y=2000(20)+40,000 y=40,000+40,000 = 80,000