Below is a table which can be used to convert between meters and feet. Part a) Use the information in the table to draw a conversion graph. Part b) Which distance is shorter? 10 meters or 35 feet. You must show your working.
In order to actually answer part a), what we need to do is actually draw our conversion graph. To do this, we’re going to need to plot the points we’ve been given in our table. We’ve got meters, which are actually our 𝑥-coordinates, because they’re on the 𝑥-axis, and feet, which are our 𝑦-coordinates, because feet is on the 𝑦-axis.
Now before we can actually plot the points, what we need to do is actually add a scale onto the 𝑥-axis. And I’ve done that here. So we’ve got five, 10, 15, 20. And I needed to use this scale because the maximum number of meters is 18. The key when adding your scale is to make sure that there’s even spacing. So I’ve done that because I can see that each of the big squares is worth five.
Okay, great, now let’s plot our points. So the first point is at three, 10. The second point is six, 20, so six meters, so six along the 𝑥-axis, and 20 feet, so 20 on the 𝑦-axis. The next point is 15, 50. And then finally, the last point is 18, 60.
So then to complete our conversion graph, what we do is actually join these points with a straight line. It goes down to zero, so the origin, and that’s because if you have zero meters, it’s going to be equal to zero feet. And we don’t extend it beyond of the top point that we have, which is 18, 60. So now that’s part a) completed, because we’ve drawn our conversion graph.
Okay, so now we’re gonna move on to part b). And in part b), what we’re going to do is use our conversion graph, because what we can use it for is to actually convert between meters and feet.
In part b), we want to find out which distance is shorter: 10 meters or 35 feet. So in order to work this out, what we need to do is work out how much 10 meters is in feet. And to do this, I’ve actually drawn a dotted line up from 10 on the 𝑥-axis, because that’s meters, and it goes along to the 𝑦-axis where the feet are.
And we can see that 10 meters is approximately 33 feet. And I’ve got that because actually each of the very small squares is worth one feet. So therefore, it’s three squares up on the 𝑦-axis from the 30, which would make it 33 feet. Well, 33 feet is less than 35 feet. So therefore, as 10 meters is approximately equal to 33 feet, then therefore 10 meters must be shorter than 35 feet.