Question

ada is filling a bucket with water. the graph shows the relationship between the amount of water in the bucket, w, and time passed, t. select all the true statements. the bucket fills at a rate of 2 liters per minute. the bucket fills at a rate of 10 liters per minute. the bucket starts with 10 liters of water in it. the relationship is proportional. the relationship is linear.

Explanation:

1. Analyze the equation \( w = 10 + 2t \):

• The slope (rate of filling) is 2, so the bucket fills at 2 liters per minute (supports "The bucket fills at a rate of 2 liters per minute").
• When \( t = 0 \), \( w = 10 \), so the bucket starts with 10 liters (supports "The bucket starts with 10 liters of water in it").
• The equation is linear (in the form \( y = mx + b \)), so the relationship is linear (supports "The relationship is linear").
• A proportional relationship has the form \( y = kx \) (no constant term), but here \( w = 10 + 2t \) has a constant term (10), so it is not proportional (eliminates "The relationship is proportional").
• The rate is 2, not 10 (eliminates "The bucket fills at a rate of 10 liters per minute").

Answer:

• The bucket fills at a rate of 2 liters per minute
• The bucket starts with 10 liters of water in it
• The relationship is linear