[Music] 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 a mountain 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 you by putting this proportional symbol between hours worked and amounts earned this means that if you worked one hour and got paid 12 pounds then if you worked two hours which is twice as long you'll get paid twice as much so 24 pounds or if you worked 10 times as long so 10 hours then you'd get paid 10 times as much so 120 pounds 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 at two it passes through the origin which is this point at zero zero if we label our axis with hours worked and money earned we can see that one hour corresponds to 12 pounds 2 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 three and a half hours which we could show with this vertical line then by tracing a line across the y-axis we can see that you would earn 42 pounds so to summarize 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 so if you found it useful then please do give us a like and subscribe and thanks for watching