Analyzing Graphs and Equations

The video tutorial covers two main problems. The first involves calculating how many gallons remain in a smaller pool after both a larger and smaller pool are drained at the same rate by pumps. The second problem involves analyzing a graph to determine the best equation that models the relationship between distance and time for bus routes. The tutorial also includes solving for a variable in a linear equation using given points on a graph.

What is the initial task in the pool draining problem?

• Calculate the total time to drain both pools.

• Determine the rate at which the pumps drain water.

• Find out how many gallons are left in the smaller pool when the larger pool is drained.

• Estimate the cost of draining the pools.

How many gallons per minute do four pumps drain?

• x gallons per minute

• 2x gallons per minute

• 4x gallons per minute

• 8x gallons per minute

How long does it take to drain the 5,400-gallon pool using four pumps?

• 540/x minutes

• 540 minutes

• 1,350/x minutes

• 1,350 minutes

How many gallons are left in the smaller pool after the larger pool is drained?

• 2,700 gallons

• 1,300 gallons

• 700 gallons

• 4,000 gallons

What does the graph in the second problem represent?

• The relationship between fuel consumption and distance.

• The relationship between distance and time for bus routes.

• The relationship between cost and time for a project.

• The relationship between speed and time for a car.

Which equation best models the relationship between distance and time for the bus routes?

• t = 2d + 10

• t = 2d

• t = d + 10

• t = d

What is the slope of the line in the equation wx + 4y = -12?

• w/4

• -4/w

• 4/w

• -w/4

What is the value of w in the equation wx + 4y = -12?

• 6

• 5

• 3

• 4

What is the change in y when x changes from -4 to 0 in the graph?

• 5

• -5

• -3

• 3

What is the equation of the line in y = mx + b form for wx + 4y = -12?

• y = 4/wx - 3

• y = -4/wx + 3

• y = w/4x + 3

• y = -w/4x - 3