Proportional relationships
Linear relationships
Solving for x
Scenarios --> equations
100

What are the defining characteristics of the graph of a proportional relationship?

The graph of a proportional relationship is a straight line and goes through the origin.

100

What is a linear relationship? Come up with as detailed of an explanation as possible. 

A linear relationship is a relationship where there is a constant rate of change, and it is represented as line. Example: y = 2x + 2

100

x + 9 = 17

x = 8

100

SLC 15 starts the week with 250 SLC points and gets 100 each day. What is the equation that represents the number of SLC points, y, after x days?

y = 100x + 250

200

What is the equation to represent a proportional relationship? 

y = kx

200

What is the equation for representing a linear relationship, and what do each of the variables mean? 

The equation is y = mx + b. "m" is the slope of the line or the rate of change, and "b" is the y-intercept, or what you start with. 
200

x - 8 = 19

x = 27

200

Teacher Sophie is planning activities for class and has planned 2 already. She creates 7 more activities per day. What equation represents the number of activities, y, after x days?

y = 7x + 2

300

What is a constant of proportionality?

A constant of proportionality is the rate of change for a proportional relationship.

300
Is the equation y = 3x linear? Why or why not? 

The equation y = 3x is linear, because it has a constant rate of change of 3. Even though it goes through the origin, it is still linear.

300

x + 5 = 27

x = 22

300

Bariq is at the starting line of a race and runs 20 meters every minute. What equation represents his distance from the starting line, y, after x minutes?

y = 20x

400

Is the equation y = 3x + 7 proportional or not?

It is not! A proportional relationship has to go through the origin, which means that its y-intercept has to be 0.

400

For the equation y = 14x + 8, what is the slope? What is the y-intercept?

Slope = 14, y-intercept = 8

400

x - 16 = 31

x = 47

400

Noah is solving math problems, and he has solved 5 already. Every day, he solves 10 more. What is the equation that represents the number of math problems, y, completed after x *weeks*?

y = 50x + 5

500

Take 30 seconds and write a scenario that represents a proportional relationship. 

Your scenario should have a constant rate of change, and the y-intercept should be zero.

500

In 30 seconds, write a scenario that represents a linear relationship.

Your answer should include a constant rate of change and a starting value.
500

x - 4 + 17 = 10

x = -3

500

SLC 16 is doing a whiteboard race activity to complete math problems, and they have already completed 17. They complete 5 problems every ten minutes. What is the equation to represent the number of problems, y, solved after x *hours*?

y = 30x + 17

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