Linear Equations and Linear Systems

Linear Equations

100

All proportional relationships go through the ___, therefore they have a ___. 

origin, constant 

200

In y=mx+b, m is ___ and b is ___. 

slope, y-intercept

300

If you have parenthesis in a multi-step equation, you need to use the ____ ____. 

distributive property

400

What operations do we need to use in last step in order to isolate the variable? 

multiplication or division

How many solutions?

100

y=3x+3

y=3x+3

infinite solutions

200

y=4x+6

y=4x+10

no solution

300

y=8x+10

y=2x+10

one solution

400

y=-3x

6x+2y=6

no solution

Substitution

100

y=2

y=3x+6

What does x equal? 

12

200

y=5x

5x+2y=15

What does x equal? 

1

Real-world scenarios

100

Yesterday, your friend watched 5 episodes of Friends yesterday and you watched 2 episodes. Today, you both watch one episode per hour. Will you ever catch up? 

No

200

Yesterday, your friend watched 5 episodes of Friends yesterday and you watched 2 episodes. Today, your friend watches 3 per hour and you watch 1 per hour. What are the two equations in the linear system. 

y=3x+5

y=x+2