The term directly proportional means that as one variable increases, another variable increases at the same rate. For example, imagine that we were comparing hours worked to amount earned. As long as you were being paid the same amount each hour, then these two variables or values can be considered directly proportional, which we can show by putting this proportional symbol between hours worked and amount earned. This means that if you worked one hour and got paid £12, then if you worked two hours, which is twice as long, you would get paid twice as much, so £24.
Or if you worked ten times as long, so ten hours, then you would get paid ten times as much, so £120. Now, if we plot a direct proportion relationship like this on a graph, then it will always look like this. And the two really important points to notice here are that one, it's a straight line, it's not curved at all, and that two, it passes through the origin, which is this point at.
If we label our axes with hours worked and money earned, we can see that one hour corresponds to 12 pounds, two hours corresponds to 24 pounds, and so on. And so we can use graphs like this to find out how much you would earn in any particular length of time. For example, if you worked 3 and a half hours, which we could show with this vertical line, then by tracing a line across to the y-axis, we can see that you would earn £42. So to summarise, the main takeaway of this video is that if two variables are directly proportional to each other, then they'll both increase or decrease proportionally.
So if one doubles, the other one doubles, or if one halves, the other one halves. And when we plot these both on a graph, it will always look like this, with a straight line that passes through the origin. Anyway, that's everything for this video.
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