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Brendan Holmes Presents: An Educational Presentation Direct Variation • Has no fixed cost. • Has x and y values. • Uses the formula: y=mx, where m is the Constant of Variation. • On a graph, it: - is a straight line - passes through the origin Click Here Direct Variation Example #1 • • Patrick Kane and Jonathan Toews were fighting with the team mascot, so they were forced to clean up the garbage in the stands for community service. For every hour that they cleaned, they needed to pick up 45 pieces of garbage. Complete a table of values to see how much garbage they had picked up after 7 hours. Therefore, they picked up 315 pieces of garbage after 7 hours. Hours (x) Equation Garbage (y) 0 1 2 3 4 5 6 7 Y=45(0) Y=45(1) Y=45(2) Y=45(3) Y=45(4) Y=45(5) Y=45(6) Y=45(7) 0 45 90 135 180 225 270 315 Direct Variation Example #2 • • The Ancaster High School Triathlon was accepting donations from the teams. Each team gave $34. Complete a table of values to see how much money was raised by 6 teams. Therefore, $204 was raised by 6 teams. Teams (x) Equation Money in $ (y) 0 1 2 3 4 5 6 Y=34(0) $0 $34 $68 $102 $136 $170 $204 Y=34(1) Y=34(2) Y=34(3) Y=34(4) Y=34(5) Y=34(6) Partial Variation • Has a fixed cost. • Has x and y values. • Uses the formula: y=mx+b, where m is the Constant of Variation, and b is the Fixed Cost. • On a graph it: - is a straight line - Does not pass through the origin Partial Variation Example #1 • • A group of kids were selling Kool-Aid for $1.75 a bottle.They started off with $14. Complete the table of values to find how much money the kids earned if 6 people bought their Kool-Aid. Therefore, the kids have earned $24.50 if 6 people bought their Kool-Aid. # of Kids (x) 0 1 2 3 4 5 6 Equation Y=1.75(0)+14 Y=1.75(1)+14 Y=1.75(2)+14 Y=1.75(3)+14 Y=1.75(4)+14 Y=1.75(5)+14 Y=1.75(6)+14 Money Earned (y) $14 $15.75 $17.50 $19.25 $21.00 $22.75 $24.50