Writing Equations for Proportional Relationships from Graphs

What is the key characteristic of a proportional relationship graph?

• It has a constant rate of change and starts at the origin.

• It has a variable rate of change and starts at any point.

• It has a variable rate of change and starts at the origin.

• It has a constant rate of change and starts at any point.

In the equation y = kx, what does 'k' represent?

• The x-intercept

• The slope of the line

• The y-intercept

• The constant of proportionality

If a graph shows 2 ounces of dark chocolate for every 6 ounces of almonds, what is the constant ratio?

• 1:3

• 2:6

• 6:2

• 3:1

What is the simplified form of the ratio 6:2?

• 3:1

• 6:2

• 1:3

• 2:6

In the example of Jackie's garden, what is the constant ratio of carrots to square feet?

• 1:9

• 9:1

• 9:9

• 1:1

What does the equation y = 9x represent in the context of Jackie's garden?

• Every square foot allows 9 carrots to be grown.

• Every 9 square feet allows 1 carrot to be grown.

• Every square foot allows 1 carrot to be grown.

• Every 9 square feet allows 9 carrots to be grown.

What is a key indicator that a graph is not proportional?

• It has a variable rate of change.

• It has a constant rate of change.

• It does not start at the origin.

• It starts at the origin.

Why can't a graph be proportional if it doesn't start at the origin?

• Because the ratio y/x would not be constant.

• Because the graph would have a variable rate of change.

• Because the ratio y/x would be constant.

• Because the graph would be a straight line.

In the challenge zone example, what is the constant ratio of dollars raised per lap?

• 100

• 25

• 32

• 800

What does the equation y = 32x represent in the context of the challenge zone example?

• Every lap raises 32 dollars.

• Every 32 laps raise 1 dollar.

• Every lap raises 25 dollars.

• Every 25 laps raise 32 dollars.