Algebra 1
UNIT 2
Formulas and Functions
OBJECTIVES:
1) Solve formulas for different variables.
2) Solve equations for y so that y is a function 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 Formula
Solve for r in d = rt
d = rt
Rewrite original formula
t
t
Isolate r by dividing both sides by t
d
r
t
Example problem:
If you ride your bike
for 2.5 hours and
travel 37.5 miles, what
is your average
speed?
Interest Formula
Solve I = prt for r.
I = prt
Rewrite the original formula
pt pt
Isolate r by dividing by pt
I
r
pt
Example problem:
Find the rate when $2800
was invested for 4 years and
earned $504 Interest.
Area of a Prism Formula
Solve for B.
S = 2B + Ph
S = 2B + Ph
-Ph
- Ph
S - Ph = 2B
_____________
2
Write original formula
Subtract Ph from each side
______
2
Isolate B by dividing both sides by 2
S - Ph = B
2
Practice Problems
1)
Solve for w : V  lwh
1
2) Solve for b : A  bh
2
V lwh

lh lh
v
w
lh
1 2
2
  A  bh 
2 1
1
2 A bh

h
h
2A
b
h
Rewriting an Equation
in Function Form
Rewrite the equation so y is a function of x.
6y - 12x = 18
6y - 12x = 18
+12x
+12x
6y
= 12x + 18
______
6
________
6
________
6
y= 2x+3
Rewrite the original equation
Add 12x to both sides
Divide both sides by 6
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
2
y  x5
3
Divide both sides by -3
-
Practice Problems
1)
4 x  3 y  12
4 x  3 y  12
 4x
 4x
3 y  4 x 12


3
3
3
4
y  x4
3
2) 2( y  2)  x  4
2( y  2)  x  4
2y  4  x  4
4
2y
2
4
x

2
1
y x
2