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:

Step1: Analyze the equation \( w = 10 + 2t \)

The equation is in the form of a linear equation \( y = mx + b \), where \( m \) is the slope (rate) and \( b \) is the y - intercept (initial value). Here, \( w = 2t+ 10 \), so it is a linear relationship.

Step2: Check the rate of filling

In the equation \( w = 10 + 2t \), the coefficient of \( t \) (time) is 2. This means that for each unit increase in \( t \) (per minute), \( w \) (water in bucket) increases by 2 liters. So the bucket fills at a rate of 2 liters per minute.

Step3: Check the initial amount of water

When \( t = 0 \) (time = 0, at the start), we substitute \( t = 0 \) into the equation \( w=10 + 2(0)=10 \). So the bucket starts with 10 liters of water.

Step4: Check if the relationship is proportional

A proportional relationship has the form \( y = kx \) (passes through the origin, \( b = 0 \)). Our equation is \( w=10 + 2t \), where \( b = 10
eq0 \), so it is not a proportional relationship.

Step5: Confirm linear relationship

Since the equation is in the form of a linear equation (\( w=2t + 10 \)), the relationship between \( w \) and \( t \) is linear.

Answer:

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