Maths Misc. Problems

1. Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 30 liters per minute. There are 600 liters in the pond to start.
Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.

2. A line passes through the point (3, -1) and has a slope of -3. Write an equation for this line.

3. Write equations for the horizontal and vertical lines passing through the point (4, -9)

4. Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.55 
If the monthly cost for 24 HCF is $44.84, what is the monthly cost for 30 HCF?

5.Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2066 pounds. When carrying 42 gallons of fuel, it weighs 2231 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?

6. Consider the line y=-5x+1
Find the equation of the line that is parallel to this line and passes through the point (-7,6)
Find the equation of the line that is perpendicular to this line and passes through the point(-7,6)

7. A line passes through the point (1,2) and has a slope of 9. Write an equation for this line.

8. Write equations for the vertical and horizontal lines passing through the point (1,9)

9. The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5 
Suppose that the height of the candle after 13 hours 19.5 centimeters. What was the height of the candle after 6 hours?

10. Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 15 hours hours of burning, a candle has a height of 21. 5 centimeters. After 26 hours of burning, its height is 16 centimeters. What is the height of the candle after 21 hours?

11. Consider the line y=-9x+2
Find the equation of the line that is parallel to this line and passes through the point(3,5)
Find the equation of the line that is perpendicular to this line and passes through the point(3,5)