1. 2.5 Linear Equations and Formulas: Linear Equation: An equation that produces a line on a graph. Literal Equation: An equation that involves two or more variables. 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 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: let y be the number of Sandwiches $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, $10x + $5y = $80 that is ISOLATE the y: -$10x $5y = -$10x + $80 ____ ____ ____ $5 $5 $5 y = -2x + 16 Subtract $10x Divide by $5

5. We now know the literal equation to find the number of Sandwiches depending on the number of Pizzas we order: y = -2(4) + 16 y = -2x + 16 Substitute x for 4 Multiplication Our original problem ask us to order 4 Pizzas (x=4) and find out the number of sandwiches we can buy: y = -2x + 16 y = -8 + 16Addition 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 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: let y represent his second job $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: $11x + $8y = $150 that is ISOLATE the y: -$11x $8y = -$11x + $150 ___ ____ ____ $8 $8 $8 y = -11x + 150 8 8 Subtract $11x Divide by $8

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

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

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

13. YOU TRY IT:

14. Solution: 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/rati onal-expressions/solving-rational- equations/v/solving-rational-equations-2 https://www.khanacademy.org/math/algebra/ratio nal-expressions/solving-rational- equations/v/rational-equations

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