Rosita and Garth are saving up for a vacation, and begin with a certain amount saved each. If Rosita works 5 hours, she will hav
e $128. If she works 7 hours, she will have $164. If Garth works 3 hours, he will have $124. If he works 8 hours, he will have $194. They want to know when they will have saved the same amount of money and how much each will have saved.
Treat each (time, money) pair as an (x, y) pair, and get the slope of the line: For Rosita, (5, 128), (7, 164): m = (y2 - y1)/(x2 - x1) = (164 - 128)/(7 - 5) = 18, implying that she earns $18/hr. The y-intercept is calculated as: y = 18x + b, 128 = 18*5 + b, b = $38, meaning that she started with $38. Rosita's equation is y = 18x + 38. For Garth, (3, 124), (8, 194): m = (194 - 124)/(8 - 3) = 14. For 124 = 14*3 + b, b = $82. Garth's equation is y = 14x + 82
To find out when they will have saved the same amount, both equations would have the same y-value: 18x + 38 = 14x + 82 4x = 44 x = 11 hours y = 18*11 + 38 = $236 (alternatively, y = 14*11 + 82 = 236) This means that Rosita and Garth will have both saved $236 after 11 hours of working.
