Algebra 1Algebra 1UNIT 2UNIT 2

Formulas and Formulas and FunctionsFunctions

OBJECTIVES:OBJECTIVES:1)1)Solve formulas for different variables.Solve formulas for different variables.2)2)Solve equations for y so that y is a function Solve equations for y so that y is a function of x.of x.

Vocabulary• Formula - an algebraic equation that relates 2 or more real life quantities

• Example: V = lwh (volume of a rectangle)• Non-Example: 2x + y = 3

• Function Form – An equation solved for y so that y is a function of x.

• Example: y = -7x + 3• Non-example: -4x + 2y = 5

Distance FormulaSolve for r in d = rt

d = rt Rewrite original formula t t Isolate r by dividing both sides

by t Example problem:

If you ride your bike for 2.5 hours and travel 37.5 miles, what is your average speed?

d rt

Interest FormulaSolve I = prt for r.

I = prt Rewrite the original formulapt pt Isolate r by dividing by pt

Example problem:Find the rate when $2800 was invested for 4 years and earned $504 Interest.

rptI

Area of a Prism Formula Solve for B. S = 2B + Ph

S = 2B + Ph Write original formula -Ph - Ph Subtract Ph from each side S - Ph = 2B _____________ ______

2 2 Isolate B by dividing both sides by 2

S - Ph = B 2

Practice Problems1) lwhVwforSolve :

2) bhAbforSolve21:

wlhv

lhlwh

lhV

bhA

hbh

hA

bhA

2

212

21

12

Rewriting an Equation in Function Form

Rewrite the equation so y is a function of x. 6y - 12x = 18

6y - 12x = 18 Rewrite the original equation

+12x +12x Add 12x to both sides6y = 12x + 18 ______ ________ ________

6 6 6 Divide both sides by 6

y = 2 x + 3

Rewriting an Equation in Function Form

Rewrite the equation so y is a function of x. -3y + 2x = 15

-3y + 2x = 15 Rewrite the original equation -2x -2x Subtract 2x to both sides-3y = -2x + 15 ______ _______ _______

-3 -3 -3 Divide both sides by -3

532

xy

Practice Problems1) 1234 yx 2)

434

312

34

33

441234

xy

xyxx

yx

4)2(2 xy

xy

xy

xyxy

2122

2444424)2(2