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)

GOAL:

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

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 -$10x $5y = -$10x + $80 ____ ____ ____ $5 $5 $5

y = -2x + 16

Subtract $10x

Divide by $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 + 16 Addition y = 8

Therefore, if we buy 4 pizzas, we can also buy 8 sandwiches.

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?

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

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 -$11x $8y = -$11x + $150

___ ____ ____ $8 $8 $8

y = -11x + 150 8 8

Subtract $11x

Divide by $8

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 8y = -77 + 150 8 8y = 73 8

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 xDivide by (a-b)

Get the variable on the same side

ax = c + bx-bx -bx

ax – bx = c

x(a– b) = c______ ____ (a– b) (a– b) X =

YOU TRY IT:

How is the area of triangle related to the height?

( A = ½bh)

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 h =

The height of a triangle is twice the area of the triangle divided by the base.

YOU TRY IT:

How do we convert Degrees Celsius into Degrees Fahrenheit?

(C)

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.

VIDEOS: Multi-Step Equations

Rational Equations

https://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/solving-rational-equations-2

https://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/rational-equations

CLASSWORK:

Page 112-114

Problems: As many as it takes for your to master the concept.