Linear Equations – Formulas
Evaluating Formulas
When evaluating formulas, we substitute the given value for the
appropriate variable and then solve for the remaining unknown
variable.
Example 1:
Distance traveled is given by
d=r·t
where r is the rate (miles per hour, feet per second, etc.) and t is the time
(hours, minutes, seconds, etc.). Find the distance traveled if a vehicle
was driven for 3 hours at a speed (rate) of 75 mph.
d=r·t
d = (75) (3)
d = 225
Substitute the values r = 75 and t = 3
The distance traveled is 225 miles.
Example 2:
The area of a trapezoid is given by
where h is the height, a is a base, and b is the other base. Find the area
of a trapezoid with bases 10 cm and 15 cm, and height 8 cm.
Modified from Introductory Algebra, by Andrew Gloag and Anne Gloag, CC-BY 2012, CK-12 Foundation,
www.ck12.org. Licensed under a Creative Commons Attribution 3.0 Unported License
(http://creativecommons.org/licenses/by-nc-sa/3.0)
a=10 cm
h=8 cm
b=15 cm
Substitute the values h=8, a=10, and b=15
Simplify:
and (10 + 15) = 25
The area of the trapezoid is 100 cm2
Example 3:
The area of a circle is given by
where r is the radius and π is 3.14 (rounded). Find the area of a circle
with radius 17 inches.
Substitute the values π = 3.14 and r = 17
The area of the circle is 907.46 in2
Modified from Introductory Algebra, by Andrew Gloag and Anne Gloag, CC-BY 2012, CK-12 Foundation,
www.ck12.org. Licensed under a Creative Commons Attribution 3.0 Unported License
(http://creativecommons.org/licenses/by-nc-sa/3.0)
Solve a Formula for a Given Variable
Solving formulas for a given variable is much like solving
general linear equations. The only difference is we will have
several variables in the problem, and we will be attempting to
solve for one specific variable. We will “move” the variables as
we would numbers.
Example 4:
Solve the formula A = LW for W
A = LW
L
L
Divide both sides by L
=W
Example 5:
Solve the formula y = mx + b for m
y = mx + b
-b
-b
y – b = mx
x
x
Subtract b from both sides
Divide both sides by x
=m
Modified from Beginning and Intermediate Algebra, by Tyler Wallace, CC-BY 2010. Licensed under a
Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0)
Example 6:
Solve the formula a =
for b
a=
(2 – b) a =
(2 – b)
(2 – b) a = A
2a – ab = A
- 2a
- 2a
- ab = A – 2a
-a
-a
Multiply each term by (2 – b)
Distribute a through parentheses
Subtract 2a from both sides
Divide both sides by –a
b=
Modified from Beginning and Intermediate Algebra, by Tyler Wallace, CC-BY 2010. Licensed under a
Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0)