Check it out!
1
3.1.1: Graphing the Set of All Solutions
Mallory had $1 this morning and asked her mom for
another. Instead of giving Mallory more money, her mom
said she would give Mallory $2 the next day if she still
had the dollar she was holding. Plus, she would continue
to give Mallory $2 each day as long as she saved it all.
Mallory agreed to the deal and began to wonder how
much money she might have at the end of the week. To
find out, Mallory graphed the equation y = 2x + 1, shown
on the next slide.
2
3.1.1: Graphing the Set of All Solutions
Dollars
Days
3.1.1: Graphing the Set of All Solutions
3
1. If today, Day 0, is Monday and x is in days, how much
could Mallory have on Wednesday?
1. How much could Mallory have on Friday?
1. How does the graph represent Mallory’s mother
giving her $2 each day?
4
3.1.1: Graphing the Set of All Solutions
1. If today, Day 0, is Monday and x is in days, how much
could Mallory have on Wednesday?
• If Monday is 0, Wednesday is 2. Substitute this
value into the equation Mallory used.
y = 2x + 1
y = 2(2) + 1 = $5
Equation
Substitute 2 for x.
• Mallory could have $5 on Wednesday.
5
3.1.1: Graphing the Set of All Solutions
2. How much could Mallory have on Friday?
• Friday is Day 4 on the graph. Substitute this value
into the equation.
y = 2x + 1
y = 2(4) + 1 = $9
Equation
Substitute 4 for x.
• Mallory could have $9 on Friday.
6
3.1.1: Graphing the Set of All Solutions
3. How does the graph represent Mallory’s mother
giving her $2 each day?
• The slope of the graph is 2. The graph shows that
Mallory can receive $2 on the y-axis for every
1 day on the x-axis.
7
3.1.1: Graphing the Set of All Solutions