Graphing linear functions example 1 | Algebra I | Khan Academy — Transcript

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1. 0:00- [Voiceover] Karl filled up the tank of his truck
2. 0:02with 400 liters of fuel and set out to deliver
3. 0:05a shipment of bananas to Alaska.
4. 0:07The truck consumed 0.8 liters of fuel
5. 0:11or eight-tenths of a liter of fuel
6. 0:13for each kilometer driven.
7. 0:15Graph the amount of fuel remaining in the truck's tank
8. 0:18in liters as a function of distance
9. 0:21driven in kilometers.
10. 0:23And right over here we have, we have a graph
11. 0:27where we have a coordinate plane
12. 0:28where our horizontal coordinate is distance in kilometers,
13. 0:32and our vertical, our vertical axis is fuel in liters.
14. 0:37So we can define the line by moving these two points around,
15. 0:41because two points define a line.
16. 0:43And so, let's just think about two points
17. 0:45that we could figure out.
18. 0:46Can we figure out the fuel at two different distances,
19. 0:49and then that will help us define the line.
20. 0:52Well, the first thing that we might want to think about
21. 0:54is, well, what about before we've traveled at all?
22. 0:57That might be the easy thing to figure out.
23. 0:59What was the amount of fuel in the tank
24. 1:01when we haven't traveled at all?
25. 1:03And they tell us that in this passage.
26. 1:06And I encourage you to pause the video and think about that.
27. 1:09Well, they tell us Karl filled up the tank of his truck
28. 1:12with 400 liters of fuel and then set out to deliver
29. 1:15a shipment of bananas.
30. 1:17So before he had driven at all,
31. 1:18right after he'd filled his tank,
32. 1:20he had 400 liters of fuel.
33. 1:23So we could say when distance was zero kilometers,
34. 1:26he had 400 liters of fuel.
35. 1:28So we have one point on that line.
36. 1:30Now we gotta think about where we might want to put,
37. 1:32where we want to put this other point.
38. 1:34And the way I think about it is,
39. 1:36well, let's just, we know he's consuming,
40. 1:38he's consuming eight-tenths of a liter of fuel
41. 1:42for each kilometer driven.
42. 1:44But they don't have, you know, we're not going by
43. 1:46one kilometer, two kilometers.
44. 1:47They're going by, this is like
45. 1:4850 kilometers, 100 kilometers.
46. 1:50So let's think about how much fuel
47. 1:52he would have consumed after driving 100 kilometers,
48. 1:56and if he consumed that much, we would subtract that
49. 1:58from the amount of fuel he started with,
50. 2:00and then that would tell us,
51. 2:01that would tell us where this point would be.
52. 2:03It's going to be some place over here,
53. 2:05and it's going to be, it's going to be below 400,
54. 2:07'cause we're consuming fuel.
55. 2:09Fuel should be going down as distance increases.
56. 2:12This should be a downward-sloping line.
57. 2:16So I have my, I have my scratchpad here.
58. 2:18Let me, let me get it out.
59. 2:20And I have the same question there.
60. 2:21It just gives us all the same information.
61. 2:24But what I want to figure out is, so we already know,
62. 2:27we already know that.
63. 2:29So we have distance, distance.
64. 2:33Let me, I'll just write.
65. 2:35Actually, let me just write the whole thing.
66. 2:37Give myself a little bit more space.
67. 2:39Distance in kilometers. Distance in kilometers.
68. 2:43And then you have fuel,
69. 2:45you have fuel in liters.
70. 2:49You have fuel in liters.
71. 2:51And we already figured out that
72. 2:52before he got on, right after he filled up his tank
73. 2:54but before he set out on his trip,
74. 2:57at distance zero kilometers he had 400 liters of fuel.
75. 3:01And we've already actually plotted that.
76. 3:04But then we said, well what happens at a hundred kilometers?
77. 3:07At a hundred kilometers, how much fuel will he have?
78. 3:10Well, they tell us that he consumes 0.8 liters of fuel
79. 3:15for each kilometer.
80. 3:16So, 0.8 liters
81. 3:20per kilometer, and then we just multiply that
82. 3:23times the number of kilometers.
83. 3:25So, times 100 kilometers.
84. 3:29The units work out, kilometers divided by kilometers.
85. 3:32We're just going to be left with liters,
86. 3:33and then we multiply the numbers.
87. 3:35Eight-tenths of a hundred,
88. 3:37well that's going to be equal to 80,
89. 3:39and the units are liters, 80 liters.
90. 3:43So at a distance of a hundred kilometers,
91. 3:45he's going to have consumed, right,
92. 3:47let me be careful here.
93. 3:48He's going to have consumed 80 liters.
94. 3:51He's going to have consumed 80 liters.
95. 3:53So the fuel, the fuel is actually going to be
96. 3:57what he started with, what he started with
97. 4:00minus how much he consumed.
98. 4:03So it's going to be minus 0.8,
99. 4:06and if we want to write the units there.
100. 4:07I might as well, so, you know, this is liters
101. 4:10right over here.
102. 4:11This is 400 liters.
103. 4:13And I can write this kilometers, kilometers.
104. 4:16It's going to be 400 liters
105. 4:18minus 0.8 liters
106. 4:23per kilometer times, times,
107. 4:27let me make that clear,
108. 4:28times 100, times 100 kilometers.
109. 4:34And same thing, kilometers divided by kilometers,
110. 4:36and we are left with 400 liters minus 0.8 liters times 100.
111. 4:41Well, that's just going to be equal to 400 liters,
112. 4:45which is how much he started with,
113. 4:46minus eight-tenths of a hundred is 80,
114. 4:49and the units left is 80 liters.
115. 4:52So 400 liters minus 80 liters,
116. 4:54that's going to be 320 liters.
117. 4:56So when he has traveled a hundred kilometers,
118. 4:59he will have 320 liters left in his tank.
119. 5:03So let's plot that.
120. 5:04So when he has traveled a hundred kilometers,
121. 5:05actually, I just randomly had put the point there,
122. 5:08he is going to have 320 liters left in his tank.
123. 5:11And just like that, we have plotted the line that showed
124. 5:15how much fuel he has in his tank
125. 5:16as a function of, as a function of distance traveled.
126. 5:21And you can even see from this
127. 5:22that he's going to run out of fuel
128. 5:24at the 500-kilometer mark.