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# Linear function example: spending money

## Video transcript

Jill just received \$40 the number of dollars she has left why after X days is approximated by the formula y is equal to 40 minus 2.5 X graph the equation and use the graph to estimate how much money Jill will have 8 days later so let's just make a table of x and y values then we can use that table to actually plot the graph and then ask us to do everything else they want us how much money she'll have after 8 days we could actually just put that right in the equation we might as well do that so we're doing numbers of days we're not going to go back in time she starts with \$40 so we can start with zero days so zero days so she just receives \$40 you don't have to look at the equation here what's the zero days after that how much money will she have well she hasn't had a chance to spend it yet so you could just think about you'll have \$40 or you could look at the equation and see that the equation verifies this when X is zero so the Y value is going to be 40 minus 2.5 times 0 which is just 40 because that part right over there is 0 so at time at 0 number of days she will have \$40 now let's do we could do one day later but then we're going to have these decimal points in here so we always so that this part of the equation all always ends up with clean numbers let's multiply it by multiples of 2 so then at two days after two days how much money will she have well it's going to be 40 minus 2 times or I'll do the same order minus 2.5 times 2 2.5 times 2 is 5 so 40 minus 5 is \$35 after 4 days it's going to be 40 let me do this in a different color so when I plot the points you see where I got my information from after 4 days she's going to have 40 minus 2.5 times 4 2.5 times 4 is 10 so 40 minus 10 is 30 you see every 2 days that goes by she is spending 5 dollars five dollars every two days or two and a half dollars everyday and you actually see that right over here she is spending that's a negative sign two and a half dollars every day every time you increment X by one two and a half dollars goes away let's keep going so then after look for another color here after six days it's going to be 40 minus 2.5 times 6 2.5 times 6 is 15 40 minus 15 is equal to 25 then finally we can do after eight days after eight days it is 40 she'll have 40 minus 2.5 times 8 2.5 times 8 is 20 so 40 minus 20 is \$20 so we actually answered your question our estimate for how much money Jill will have 8 days later is actually \$20 but let's do this first part let's actually graph the equation see it visually so let me draw some axes here this will be a hand-drawn graph but I think it'll get the job done so let's make that our y-axis or in this case it's the number of dollars she has and let's make this my x-axis this is our x-axis and we only need to focus on the first quadrant because at least in this context you won't have we're assuming she won't have a negative number of dollars so the Y values will be positive and we assume that the days are only going to be positive we're not going to deal with negative time so the X values are going to be positive so we're only going to be operating in the first quadrant so that's all I have to draw and so she starts off at \$40 so let me let me mark off the y-axis let me mark it off in increments of 10 first so this would be \$10 this would be 20 this would be 30 this would be \$40 and then I could do the the 35 the 25 the 15 and then the 5 and then let me mark off the days so this is let me do it other than that same yellow color so this is after this is after 2 days this is 4 days this is 6 days this is 8 days we could keep going if we like so after two days she after sorry after zero days so this right over here after zero days she has \$40 so that's this point right over here that's that right over there then after two days she has \$35 after two days she has \$35 - in the x-direction then we go up 35 so that's that point right over there then after 4 days she has \$30 for days \$30 you go X whar remember the days are in X or X or the days actually you market this or days and these the y axis is the dollar axis so after 4 days she has \$30.00 after 4 days she has \$30.00 then after 6 days I went to the same color after 6 days she has \$25.00 so X at x coordinate is 6 y coordinate is 25 and then finally after 8 days she has 20 dollars 8 days 20 dollars 8 she has 20 dollars and so we plotted those points we could connect them we could actually just if we had a nice ruler we could just connect two of those and we would have the line but our line looks something I'm reducing a new color our line would look something like our line would look something like that that shows how much she has after every day and we're done we have graphed the equation we know she'll have \$20 left after 8 days