Question

use the description below and the graph at the right for exercises 1 - 4.
a tank contains 5 gallons of water. joanna uses a hose to slowly add more water to the tank. five gallons of water are added to the tank every minute.

1. write an equation to describe the relationship between the number of gallons in the tank and the number of minutes the tank is being filled.
2. on the grid at the right, graph the linear relationship.
3. does it make sense to draw a line through the points? explain.
4. suppose there had been no water in the tank. how would the graph change?

for exercises 5 - 7, write an equation to represent the given linear relationship. then state the meaning of the given ordered pair.

1. renting bowling shoes costs $5. bowling costs $4 per game. (3, 17)
2. william started with 40 photographs. he took 8 more photographs each day. (6, 88)
3. monthly sales: 0, $5,000, $10,000, $15,000, $20,000

earnings: $2,000, $2,500, $3,000, $3,500, $4,000
($50,000, $7,000)

Explanation:

Step1: Identify the type of equation

The problem involves a linear relationship. The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value).

Step2: Determine the values of \(m\) and \(b\)

• The initial amount of water in the tank (\(b\)) is 5 gallons.
• The rate at which water is added (\(m\)) is 5 gallons per minute.

Step3: Write the equation

Substitute \(m = 5\) and \(b = 5\) into the linear equation \(y=mx + b\). Let \(y\) be the number of gallons of water and \(x\) be the number of minutes. The equation is \(y = 5x+5\).

Answer:

\(y = 5x + 5\)