Constant of Proportionality Worksheets
CHAPTER 4 PROPORTIONAL RELATIONSHIPS, SOLVING PROBLEMS (6 .. c Classroom Activity: Convert Units—Proportion in Tables and Graphs. Practice graphing proportional relationships with Khan Academy's free online exercises. Explore these proportion worksheets that feature exercises on solving proportions, also learn to identify if the coordinates on a graph share a proportional relationship. Form two equivalent sets of ratios from a range of 4, 5 , and 6 numbers.
At that point, the Avenger, a fast Yankee warship, received a telegram about the Serendipity's danger, and sailed from St. Bristling with cannons and marines, the warship could handle the pirates but was miles away from the ambush point. Is there enough time to catch up? Can the Avenger sail miles before the Serendipity covers 70? It's a question of proportions. Many situations in life involve proportional relationships, and sometimes the best way to understand those relationships is to draw a graph.
Two values have a proportional relationship if their ratio the fraction formed when one is divided by the other is always the same. If one doubles, so does the other. A graph is a picture of a mathematical relationship that helps us visualize how the numbers work together. It can help us look up the information we need when we have a problem involving proportions. In our example, the distance each ship has moved is proportional to how much long it has been sailing.
Figure 1 will tell us if the Avenger can travel miles before the Serendipity travels Let's take a look. Graph showing distance versus time of the two ships If you follow the blue line, which is the voyage of the Serendipity, you'll see when the ship goes 70 miles it encountered the pirates after 22 hours.
Rates & proportional relationships
What about the Avenger? Well, follow the red line to the same hour point. Did the Avenger travel miles by that time? No, at 22 hours the Avenger had only covered about miles.
It was 14 miles away when the merchant was attacked. The Avenger was too late to save the Serendipity, arriving at the scene just over an hour after the merchant vessel arrived. And notice the slope of this actual graph over here. Notice the slope of this actual graph. If our change in x is 5.
So notice, here our change in x is 5. Our change in x is 5. You see that as well. When you go from 0 to 5, this change in x is 5.
Change in x is equal to 5. What was our corresponding change in y? Well, our corresponding change in y when our change in x was 5, our change in y was equal to 2. And you see that here, when x went from 0 to 5, y went from 0 to 2. So our change in y in this circumstance is equal to 2.
Graphing proportional relationships: unit rate (video) | Khan Academy
Which if you wrote it as a decimal is equal to 0. So this right over here is your slope. So I'm going to do this with the tool. But first, let's also think about what the equation of this line is going to be. Well, we know that y is equal to some constant times x. And we know that the point 5, 2 is on this line right over here.
So we could say, well, when x is equal to 5, y is equal to 2. Or, when y equals 2, we have k times 5, or k is equal to-- dividing both sides by 5, you can't see that.
We're used to seeing this. When we have y is equal to something times x, this something right over here is going to be our slope. So the equation of the line is y is equal to 0.
So let's fill this in.
Let's actually do the exercise now. So we had two points, one was the point 0, 0. So it's y is equal to 2.
And we said the equation is y is equal to 0. So let's check our answer.