Special Linear Case: Proportional

Situations2.14

I need potatoes!• I need a whole lot of potatoes to make some delicious potato soup for a huge party

Yummy!

Two Options

Costco:

- Pay $20 membership fee

- $2 per pound of potatoes

Lucky’s:

- $4 per pound of potatoes

Let x = number of poundsLet y = total cost

Costco:

- Pay $20 membership fee

- $2 per pound of potatoes

•y = 2x + 20

Lucky’s:

- $4 per pound of potatoes

•y = 4xWhat’s different about the equation for Lucky’s?

• Costco: y = 2x + 20 • Lucky’s: y = 4x

What’s different about the graph for Lucky’s?

𝑦=23𝑥

𝑦=3 𝑥 𝑦=13𝑥

What’s true about all of these graphs?

What’s true about all of these equations?

Notes•Proportional situations: x and y coordinates create equivalent fractions

•Can rewrite as a linear equation in slope-intercept form

Vocabulary•Proportional linear equations = have an initial value (y-intercept, b) of 0

•Direct Variation = another name for a proportional relationship

• “y varies directly as x” means the graph is proportional

•Constant of Variation = the slope (m) of a proportional linear equation

Team PracticeUsing any method your team comes up with, determine if the points in the table represent a proportional relationship or not.

x 2 3 4 10y 8 12 16 40

Practice: Proportional or not?

x 3 4 5 6y 5 7 9 11

x 4 6 8 10y 6 9 12 15

x 12 15 18 24y 8 10 12 16