Writing Linear Equations
Revisited
Two Formats
• Slope intercept form: y = mx + b
• Standard form: ax + by = c
When to Use Slope Intercept
• Equations should be put into slope intercept form
anytime there is a flat fee (one time fee) and
charge per unit (item, hour, miles…etc)
– Example: Works at a car repair shop. There is a $25
garage fee and charge of $30 per hour. Write an
equation that represent the cost of having your car
repaired for any number of hours not including any
parts necessary for repair.
y = 30x + 25
When to Use Standard Form
• Equations should be put into standard form
when two quantities are related to a total.
– Example: Mark traveled a total of 1,000 miles. For
part of his trip he drove 50 mph and for other
parts of his trip he drove 60 mph. Write an
equation showing all of the speed/time
possibilities.
50x + 60y = 1,000
Deciding Which Form to Use
• Choose which form to use. You do not have to write
the equations.
• 1) Alex went to the store and purchased pineapples
and apples. Pineapples are $.99/lb and apples are
$.59/lb. He spent $5.33.
• 2) At Sam’s Thrift Store all shirts are $5 and all pants
are $7. Mario spent $43
• 3) Laser tag costs $12 per hour. Equipment rental is $6.
Deciding Which Form to Use
• 1) Alex went to the store and purchased
pineapples and apples. Pineapples are $.99/lb
and apples are $.59/lb. He spent $5.33.
Standard Form
• 2) At Sam’s Thrift Store all shirts are $5 and all
pants are $7. Mario spent $43. Standard Form
• 3) Laser tag costs $12 per hour. Equipment
rental is $6. Slope Intercept Form
Using Linear Equations
• A machine salesperson earns a base salary of
$40,000 plus a commission of $300 for every
machine he sells. Write an equation that shows
the total amount of income the salesperson
earns, if he sells x machines in a year.
• How much would the salesperson make if 20
machines were sold?
• How many machines would need to be sold to
earn $100,000 for the year?
Using Linear Equations
• A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells. Write an
equation that shows the total amount of income the
salesperson earns, if he sells x machines in a year.
y = 300x + 40,000
• How much would the salesperson make if 20 machines
were sold? y = 300(20) + 40,000 y = $46,000
• How many machines would need to be sold to earn
$100,000 for the year? (100,000) = 300x + 40,000
x = 200 machines
• At a school play, children’s tickets cost $3 each
and adult tickets cost $7 each. The total
amount of money earned from ticket sales
equals $210. Write a linear model that relates
the number of children’s tickets sold to the
number of adult tickets sold.
• How many children’s tickets were sold if 24
adult tickets were sold?
• At a school play, children’s tickets cost $3 each
and adult tickets cost $7 each. The total
amount of money earned from ticket sales
equals $210. Write a linear model that relates
the number of children’s tickets sold to the
number of adult tickets sold.
3x + 7y = 210
x = child and y = adult
• how many children’s tickets were sold if 24
adult tickets were sold? 3x + 7(24) = 210
x = 14 child tickets
• Max sells lemonade for $2 per cup and candy
for $1.50 per bar. He earns $425 selling
lemonade and candy.
• a. Write a linear model that relates the
number of cups of lemonade he sold to the
number of bars of candy he sold.
• b. If Max sold 90 bars of candy, how many
cups of lemonade did he sell?
• Max sells lemonade for $2 per cup and candy for
$1.50 per bar. He earns $425 selling lemonade
and candy.
• a. Write a linear model that relates the number of
cups of lemonade he sold to the number of bars
of candy he sold.
2x + 1.5y = 425
x = lemonade and y = candy
• b. If Max sold 90 bars of candy, how many cups of
lemonade did he sell?
2x + 1.5(90) = 425
x = 145 cups
• Mr. Thompson is on a diet. He currently
weighs 260 pounds. He loses 4 pounds per
month.
• a. Write a linear model that represents Mr.
Thompson’s weight after x months. (think
about how you would represent losing 4
pounds per month)
• b. After how many months will Mr. Thompson
reach his goal weight of 220 pounds?
• Mr. Thompson is on a diet. He currently
weighs 260 pounds. He loses 4 pounds per
month.
• a. Write a linear model that represents Mr.
Thompson’s weight after x months.
y = -4x + 260
• b. After how many months will Mr. Thompson
reach his goal weight of 220 pounds?
(220) = -4x + 260
x = 10 months