Mod 4: Review

The equation that would represent the situation: "Victoria charges $5 for each bracelet she makes".

y = 5x

The equation that would represent the situation: "Theatre tickets are $5 a person with a $10 service fee"

y = 5x +10

The equation for a proportional relationship is

y = mx or y =kx

Initial Value

y-intercept

y= 1/2x + 3

y-intercept of the equation = 3

b=-3 on this graph

y-intercept?

slope of the equation = 1/2

y= 1/2x + 3

Define proportional relationship

A linear relationship that passes through the origin and has a constant of proportionality

Linear Equation

An equation that forms a straight line when graphed

The graph must form a straight line AND the line must pass through the origin (0,0), constant rate y/x=k

How can you tell if a graph represents a proportional relationship?

y = 7x - 3 is what kind of relationship

Nonproportional equation

y = 7x is what kind of relationship

Proportional equation

Slope

Rise over run

An example of a real world situation that represents a nonproportional relationship

Sergio charges $10 an hour to babysit and a fee of $5 to travel across town.

An example of a real world situation that represents a proportional relationship

Sergio charges $10 an hour to babysit.

Constant of Proportionality (CoP)

The value of "k" in the equation y = kx. What you're multiplying by! THE SLOPE

In a table, a relationship is proportional if

There is a unit rate, you can 'see' what its multiplying or dividing by, and the ratio of y/x is all the same

Negative

Type of Slope

Positive

Type of slope

m = 3/2

What is slope of the line y = 3/2 x - 1?

m = - 3

What is the slope of the equation y = -3x -4?

m = 5

What is the slope of the equation" y=5x

m = -1

What is the slope of the equation: y = -x - 14

m = 5/3

What is the slope of the line y = 5/3 x?

b = -4

What is the y-intercept of the equation y = -3x -4?

b = -14

What is the y-intercept of the equation: y = -x - 14

b = 0

What is the y-intercept of the equation: y=5x

b = -2

What is the y-intercept of the graph?

In a table, a relationship is nonproportional if

You can NOT 'see' what is being multiplied or divided by, because the ratio of y/x is not the same

Define nonproportional relationship

has a constant rate of change and a y-intercept that is not zero ( does not go through origin)