Name: ___________________________ Per. _____EOC Ch3 J Linear Functions & Inequalities:
A1.1.B Solve problems that can be represented by linear functions, equations and inequalities.
Study Notes: There are 3 ways to solve linear equations.
 Graphically – graph each side of the equation and calculate the intersection
 Numerically – complete a table to find the solution
 Algebraically – write and equation and solve.
Strategy: Practice all 3 methods. You can check your solution with another method.
Examples
Practice
Example #1: Sue is opening an internet clothing store. For 1. A gas station’s 10,000-gallon underground
the clothes she sells, she wants to charge three times what
storage tank contains 1,000 gallons of
they cost her plus $5.00 shipping charge. What is the cost
gasoline. Tanker trucks pump gasoline into the
of the clothes if the total cost is $104?
tank at a rate of 400 gallons per minute. How
Solution:
long will it take to fill the tank?
x = the cost of the clothes
y = the total cost
a = starting value, Every total cost has a $5 shipping cost, a
=5
b = the rate of change, sue charges 3 times the cost of the
clothes, b = 3
y = 5 + 3x or 104 = 5 + 3x.
Graphically
Let f1(x) = 104 and f2(x) = 5 + 3x, set the window to
see where the graphs cross. Then menu, analysis,
intersection.
x=
y=
a=
b=
Equation:
Graphically
Numerically
Numerically
Initial cost
total cost
0
10
20
30
31
32
33
5
35
65
95
98
101
104
If the initial cost of the
clothes is $33 then the
total cost will be $104
Algebraically
Algebraically
104 = 5 + 3x
99 = 3x
x = 33
y = 104
Subtract 5 from both sides
Divide by 3
Check y = 5 + 3(33)
Name: ___________________________ Per. _____EOC Ch3 J Linear Functions & Inequalities:
A1.1.B Solve problems that can be represented by linear functions, equations and inequalities.
Study Notes: Read the problem and write an equation then change it to an inequality.
Strategy:
Examples
Example #1: You and several of your friends have
gone to a movie. Soft drinks are $2.00 and a tub of
popcorn is $6.00. You have $72.00 in your pocket.
 Write an inequality that describes how many
drink and tubs of popcorn you can buy with $72.
 Graph the inequality.
Solution: Define your variables
x= # of soft drinks
y = # of tubs of popcorn
2x is the amount you spend on soft drinks
6y is the amount you spend on popcorn
2x + 6y is the total amount you spend and it has to be
less than or equal to $72.
Practice
1. Admission to the Woodlawn Park Zoo is
$6.00 for students and $14 for adults. The
school was given a donation of $420 to go on
a field trip to the Zoo. They do not have to
spend the entire donation, but they cannot
spend more than $420.
 Write an inequality that represents
how many student and adults could
attend the field trip.
 Graph the inequality.
Solution:
x=
y=
72 > 2x + 6y
Solve the inequality for y:
2x + 6y < 72
Rewrite the inequality
6y < 72 - 2x
1
y < 12 - 3x
Solve the inequality for y:
Subtract 2x
Divide by 6
Graph the inequality
a = 12 (the y-intercept is (0, 12), this means that you
can buy 12 tubs of popcorn. A quick way to graph a
line is find one other point. If you spend $72 on $2.00
soft drinks then you could buy 36 soft drinks. (0, 36).
Use these two points to graph your line. Check the
slope of the line.
1
b= -3 (the slope is down 1 over 3)
Graph the inequality