Common Core #11 Ordered Part 2 Pairs

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Presentation transcript:

Common Core #11 Ordered Part 2 Pairs In a high school girls basketball team, one team scored 36 points but never hit a free throw. They only made 2 or 3 point goals. How many different solutions are there if you used the following expression to model their team scoring. 3x + 2y = 36

Answer 3x + 2y = 36 There are seven: (0,18), (2, 15),(4,12), (6.9), (8,6), (10, 3), and (12,0) All these ordered pairs are solutions to the equation.

COMMON CORE #11 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Is the Ordered Pair a Solution to the Equation? Is (2, 5) a solution of y = 3x + 2? What can we do to check? You can plug in the ordered pair to the equation and see if it is equal on each side.

y = 3x + 2 y = 3x + 2 Substitute (2,5) in 5 = 3(2) + 2 Work out each side 5 = 6 + 2 5 = 8 The answer is NO

What about (3, 11) y = 3x + 2 Substitute (3,11) in 11 = 3(3) + 2 Work out each side 11 = 9 + 2 11 = 11 The answer is YES

Lets Try Two More Are the points (1, 5) and (-2, 7) solutions for the following equation: y = 2x + 3 The point (1, 5) works but (-2, 7) is NOT a solution.

Board Examples Lets have four volunteers come to the board and work one of the following problems: y = 2x – 4 (1) (3, 2) (2) (-4, 5) (3) (6, 8) (4) (2, 0)

Consumer Math Application A plumbing company charges $50 for a service call and $15 per hour. Write an equation to model the situation and then find the cost for a 3 hour call. Cost = $15 per hour + $50 C = 15h + 50 Now substitute in 3 for the h C = 15(3) + 50 C = 45 + 50 C = 95 dollars The ordered pair would be (3, 95)

PRACTICE PROBLEMS Page 52 16, 18, 20, 22, 24 & 25 You will have to USE YOUR BRAIN on 25