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Use the graph to answer the questions.

The graph is illustrated as water used and the amount per minute. 5 gallons are used every minute and the gallons go from 10 - 50. The minutes go from 2 - 10. The dots on the graph are (1,5) (2,10) (3,15) (7,35) (10,50) X is the minutes Y is the gallons
Now answer these questions: a. The constant of proportionality is _______
b. Write an equation that represents the linear graph ________
c. This is a proportional relationship because the graph shows _______ .
Answers a linear relationship. 1/2. the points are connected. 2. 1. 1/5. 2y=x. 5. a constant rate of change. y=5x. linear with a y- intercept (0,0) 5y=x. 1/2y = x

1 answer

Let's analyze the information provided in your questions and the graph description step by step.

Part A: The constant of proportionality is

To find the constant of proportionality in a relationship, we need to identify the rate at which one quantity changes with respect to the other. Here, for every minute (x), there are 5 gallons of water used (y). This can be expressed as:

\[ k = \frac{y}{x} = 5 \quad \text{(where k is the constant of proportionality)} \]

Answer: 5

Part B: Write an equation that represents the linear graph

Given that the relationship is linear and proportional, the equation can be expressed in the form of \(y = kx\), where \(k\) is the constant of proportionality.

Since we determined \(k = 5\), we can write the equation as:

\[ y = 5x \]

Answer: \(y = 5x\)

Part C: This is a proportional relationship because the graph shows

A proportional relationship is characterized by a constant ratio between the quantities and passes through the origin (0, 0). The graph shows a straight line that connects the points (1,5), (2,10), (3,15), (7,35), and (10,50), all of which maintain a constant ratio of \(y\) to \(x\).

Answer: A constant rate of change (indicating it is proportional), and the points are connected in a linear fashion.

So, to summarize:

a. 5
b. \(y = 5x\)
c. A constant rate of change (indicating it is proportional), and the points are connected.