Video: Verifying Statements as True or False by Interpreting a Given Linear Graph

Based on the given graph, which statement could be true? [A] A merchant will earn $750 if he sells $15000 worth of merchandise. [B] A merchant will earn if he has no sales. [C] A merchant will earn $100 if he sells $1000 worth of merchandise. [D] A merchant will earn $3200 if he sells $3200 of merchandise.

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Video Transcript

Based on the given graph, which statement could be true? A) A merchant will earn 750 dollars if he sells 15000 dollars’ worth of merchandise. B) A merchant will earn if he has no sales. C) A merchant will earn 100 dollars if he sells 1000 dollars’ worth of merchandise. Or D) a merchant will earn 3200 dollars if he sells 3200 dollars of merchandise.

So, to solve this problem, what we’re going to do is have a look at each of the possible statements one by one. In the first statement, statement A, we’re told that a merchant will earn 750 dollars if he sells 15000 dollars’ worth of merchandise. So, it’s these two values that we’re gonna have a look at. So, first of all, if we take a look at the horizontal 𝑥-axis, we can see this is the sales in thousands of dollars. What I’ve done is I’ve marked on 15 because we got 10 and 20. So, that means halfway in-between this is gonna be 15. So, that’s gonna represent 15000 dollars’ worth of merchandise.

So, what I’ve done is drawn a dashed line up from this. And that’s because that’s our 15000 dollars’ worth of merchandise that’s been sold. And I’ve drawn it up to the point where it meets our line. So, now, what I’m gonna do is go across and see what the equivalent total earnings are going to be for this value. And when I do that, I can see that if I’ve drawn my dashed pink line across to the corresponding place on our 𝑦-axis, or vertical axis, we can see that it will come in at 750, so 750 dollars. This will be the total earnings.

And we’ve got that because we’ve got 1000 dollars being two squares. So therefore, one square is 500 dollars. So therefore, halfway between 500 and 1000 is 750 dollars. So therefore, we can say that statement A could be true. Okay, so that’s probably going to be our answer. We’re gonna check the other statements just to make sure.

Well, if we take a look at statement B, it says, a merchant will earn if he has no sales. Well, we can see that this won’t be true. And that’s because if you have a look at the graph, we can see that at zero sales, the total earnings is also zero dollars. So therefore, if a merchant does not sell, then a merchant will not make any money. So, statement B is false. So, it’s not gonna be the answer to the question.

Okay, great. So, now, we can move no to statement C. A merchant will earn 100 dollars if he sells 1000 dollars’ worth of merchandise. So, let’s take a look at this. So, to see if this statement is true will actually be very difficult with the scale that we’ve got. Because we haven’t got thousands on the 𝑥-axis and we haven’t got hundreds on the 𝑦-axis. So, it’ll be hard to get an accurate answer. So, what I’m gonna do is multiply both of these by 10. So, if I do that, I’ll have that a merchant will earn 1000 dollars, and that’s because 100 multiplied by 10 is 1000, if he sells 10000 dollars of merchandise. And that’s because 1000 multiplied by 10 is 10000. So, all I’ve done here is scaled it up so it’s easier to read on our graph.

So, now, you can see that as we’ve scaled it up, it actually makes it much easier to read. Because we’ve got 10000 dollars, and this is one of the points on our 𝑥-axis. So, we’ve drawn a dotted line up from here to the line of our graph. Then, we go across to our vertical axis, which is our 𝑦-axis. And we could see here that we’ve got 500 cause we found that earlier.

So therefore, from the graph, we can read and say that if a merchant sold 10000 dollars’ worth of merchandise, then they would earn 500 dollars. And therefore, if we scale this back down, we would say that if a merchant sold 1000 dollars of merchandise, then what they would earn is 50 dollars. So therefore, statement C is also untrue, or false. And I’ve just shown that calculation here. So, we got 10000 divided by 10 gives us 1000, 500 divided by 10 gives us 50.

Okay, great. Let’s move on to the final statement, statement D. Well, statement D tells us that a merchant will earn 3200 dollars if he sells 3200 dollars of merchandise. Well, we can clearly see that this cannot be true. And that’s because if we mark on our values onto our graph, well, we’ve got 3200 dollars of merchandise. Well, I’ve estimated this cause we don’t need to be too accurate.

Because it’s very clear when we go across the 𝑦-axis that if we do sell 3200 of merchandise, then the earnings is not going to be 3200 dollars. Because the earnings are less than even 500 dollars. So therefore, definitely cannot be the correct statement. So therefore, we could say that, based on the given graph, the statement that could be true is statement A. A merchant will earn 750 dollars if he sells 15000 dollars’ worth of merchandise.

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