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2.5 Linear Equations and Formulas:

Literal Equation: An equation that involves two or more variables. 2.5 Linear Equations and Formulas:. Linear Equation: An equation that produces a line on a graph. Formula: An equation that states a relationships among quantities( two equations with an equal sign ). GOAL:.

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2.5 Linear Equations and Formulas:

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  1. Literal Equation: An equation that involves two or more variables. 2.5 Linear Equations and Formulas: Linear Equation: An equation that produces a line on a graph. Formula: An equation that states a relationships among quantities(two equations with an equal sign)

  2. GOAL:

  3. We can set up a literal math equation to model the situation of the Pizza and Sandwiches as follows: Let x be the number of Pizzas we can buy and let ybe the number of Sandwiches Taking into account the price of each, $10 for Pizza and $5 for Sandwiches, we can say that the total money would be: $10x + $5y Now we only have $80 to spend in total thus: $10x + $5y =$80

  4. Furthermore, we are interested in finding our how many sandwiches we can find if we buy 4 pizzas thus we must find y in the literal equation, that is ISOLATE the y: Subtract $10x $10x + $5y =$80 -$10x -$10x Divide by $5 $5y =-$10x+ $80 ____ ____ ____ $5 $5 $5 y =-2x + 16

  5. We now know the literal equation to find the number of Sandwiches depending on the number of Pizzas we order: y =-2x + 16 Our original problem ask us to order 4 Pizzas (x=4) and find out the number of sandwiches we can buy: Substitute x for 4 y =-2x + 16 y =-2(4) + 16 Multiplication y =-8 + 16 Addition y =8 Therefore, if we buy 4 pizzas, we can also buy 8 sandwiches.

  6. REAL-WORLD: Joseph works two jobs. His first job pays him $11 per hour, while his second job only pays him $8 per hour. If Joseph has worked 7 hours on his first job, how many hours does he have to work for his second job to earn $150?

  7. We can set up a literal math equation to model Joseph’s job situation as follows: Let x represent his first job let yrepresent his second job Taking into account what he earns per hour for each job, $11 for first and $8 for the second, we have: $11x + $8y Joseph has to earn $150 in total thus: $11x + $8y =$150

  8. We are interested in finding our how many hours Joseph has to work for his second job, y, if he has already worked 7 hours for his first job: that is ISOLATE the y: Subtract $11x $11x + $8y =$150 -$11x -$11x Divide by $8 $8y =-$11x + $150 ___ ____ ____ $8 $8 $8 y =-11x + 150 8 8

  9. We now that Joseph has worked 7 hours for his first job: y =-11x + 150 8 8 y =-11(7) + 150 8 8 Substitute x for 7 y =-77 + 150 8 8 Multiplication y =73 8 Addition y = 9.125 hrs. Therefore, if Joseph has worked 7 hours for his first job, he must work 10 hrs for the second.

  10. Rewriting Literal Equations with One Variable: Ex: What equation do you get when you solve ax = c + bx for x? ax = c + bx Get the variable on the same side -bx -bx Opposite of distributing = factor the x ax – bx= c Divide by (a-b) x(a– b) = c ______ ____ (a– b) (a– b) X =

  11. YOU TRY IT: How is the area of triangle related to the height? ( A = ½bh)

  12. Solution: Remember:the formula for area of a triangle isA = ½bh and we want to isolate h: A = ½bh Isolate the h (2)A = ½bh(2) Multiply by 2 2A = bh ___ ____ b b Divide by b h = The height of a triangle is twice the area of the triangle divided by the base.

  13. YOU TRY IT: How do we convert Degrees Celsius into Degrees Fahrenheit? (C)

  14. Solution: C Given Equation C Inverse of C Inverse of - 32 F= Final equation. Thus to converts C to F we must replace the given degrees for the C.

  15. VIDEOS: Multi-Step Equations Rational Equations https://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/rational-equations https://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/solving-rational-equations-2

  16. CLASSWORK:Page 112-114 Problems: As many as it takes for your to master the concept.

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