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Interpreting Graphs - Problem 3
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
To represent a story about distance and time using a graph, start by drawing the axes and labeling time on the x-axis and distance on the y-axis. Read the story carefully to understand how the description should be translated onto the graph (i.e., how the graph will move along the two axes). When looking at graphs like this, think about how much your y value changes for every change in your x value. This will help you when you solve problems with slope.
One of the most common uses for graphs in Math class is to show distance and time. So in this problem they tell us to set up a graph with the time on the horizontal axis and distance on the vertical axis.
So I'm just going to go ahead and draw that, I know that's going to be time and distance to show how far a car travels every hour for 5 hours. So hours of course is the time measurement so I'm going to call that hours and we need to do 5 hours. If I had graph paper I would make this really precise so each hour is like exactly spaced out. Put that one over here.
Okay so I have every hour for 5 hours if it goes 60 miles per hour. That's going to be a distance thing so before we can start putting numbers on there, you might want to spend sometime and think about what that means. If you are going 60 miles an hour that means after one hour you've gone 60 miles right? After 2 hours you've gone 60 more so 120, 3 hours 180 like that. Since we are going up to 5 hours 5 times 60 gives me 300.That tells me how far I need to go up on this axis. 300 miles is the most distance I'm going to have from my 5 hours. So I'm going to go ahead and make that 100, 200, 300 miles.
Again if you have graph paper you would do this precisely. I'm just kind of doing a rough estimate but so again if you go one hour 60 miles per hour you've gone about 60 miles that's what that gap represents. If you go drive for two hours you've gone 120, three hours is 180, mark like that, four hours will be 240 and 5 hours would be 300. Those points represent the different amount of hours for the x and then distance travelled for the y etcetera.
And you'll notice it shows a perfect line. If I had done this exactly on a graph paper on like I hope you guys did, you would be able to take your ruler and draw the line that connects all those dots. Let's see how, well mine went, not great.
So mine is pretty good, mine is not perfect. If you guys use graph paper you'll see this line end up on an exactly perfect line. And the reason why is because you are going the same distance for every hour that you travel in the car. That's going to be really important when you get into the idea of slope. You want to keep in mind how much does your y number change. How much is your distance changed, and also keep in mind how much does your x number change in our case the hours.
So the last thing I want you guys to keep in mind when you are working on graphs describing word problems is how you set up your axis, I skipped by ones here I skipped by one hundreds here and also how you do the labelling this is hours, that's miles and so later on when you get into slope you'll be able to learn how the slope of this line or how steep it is represents miles per hour, 60 miles per hour.
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Sample Problems (3)
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Problem 1 7,830 views
Draw a graph with time on the horizontal axis and heart rate on the vertical axis to represent this story:Alison slept in. Then her alarm woke her up. She jumped out of bed and ran to school. Then she sat in boring classes in the morning and exciting math classes in the afternoon.
Problem 2 5,430 views
Write a story to describe what's happening in each graph:
Problem 3 4,482 views
Draw a graph with time on the horizontal axis and distance on the vertical axis to show how far a car travels every hour for 5 hours if it goes 60 miles per hour.