standard form from context

​Today we will write equations of lines in standard form. Get a dry erase marker and a calculator before you begin

​You leave the house with $30 to go to a carnival. The carnival charges $6.00 per ride and $2.00 per game. On the next slide you will start to answer:

What if you spend all of your money on games, how many could you play?

What if you spend all of your money on rides, how many can you ride?

Multiple Choice

A carnival charges $2 per game and $6 per ride. You have $30 to spend. If you only go on rides, how many can you go on?

• 5

• 6

• 15

• impossible to figure out

Multiple Choice

A carnival charges $2 per game and $6 per ride. You have $30 to spend. If you only play games, how many can you play?

• 5

• 6

• 15

• impossible to figure out

​Let's let r be rides and g be games. If you hade $30 and rides are $6 each, you can go on 5 rides because 6(5) = 30. So we can say 6r = the amount of money you will spend on rides.

Multiple Choice

If rides are $6 each, which expression did we say we can use to figure out how much we will spend on rides?

• 6r

• 5r

• 2r

• 30 - r

​Let's let r be rides and g be games. If you hade $30 and games are $2 each, you can go on 15 rides because 2(15) = 30. So we can say 2g = the amount of money you will spend on rides.

Multiple Choice

If games are $2 each, which expression did we say we can use to figure out how much we will spend on games?

• 6g

• 5g

• 2g

• 30 - g

​But what if we want to go on a few rides and play a few games. Come up with a few ways we could spend all $30 if rides are $6 each and games are $2 each.


If you need help getting started, let's say we want to go on 1 ride, how much will that cost? How many games can we play with the rest of our money?

Multiple Select

You have $30, rides are $6 each and games are $2 each. Which combinations of games and rides are possible if we want to spend all $30 at the carnival?

• 1 ride and 12 games

• 6 games and 2 rides

• 4 rides and 3 games

• 12 rides and 1 game

​we can write an expression to show how much money we will spend on rides and games:
6r + 2g

And we know we want to spend a total of $30

so we have 6r + 2g = 30.
This is called the standard form of a line

​We can make a table of all possible ways to spend our money, and graph everything in desmos.

Multiple Choice

Teachers need to transport 320 students by bus and car on a trip. If buses can hold 8 students and cars can hold 2 students, which shows the total number of buses and cars that can be used to transport the 320 students?

• 8b + 2c = 320

• 8c + 2b = 320

• 320c + 8b = 2

• 8b - 2c = 320