ada is filling a bucket with water. the graph shows the relationship between the amount of water in the…

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\neq0 ), 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.