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Problems

In Problems 1-8, find the slope and equation of the line through P and Q.

1          P(1l,2), Q (3,4)                               

2          P(1, -3), Q(0, 2)

3          P(-4, 1), Q(-4, 2)                       

4          P(2, 5), Q(2, 7)

5          P(3, 0), Q(0, 1)                               

6          P(0, 0), Q(10, 4)

7          P(1, 3), Q(3, 3)                               

8          P(6, -2), Q(1, -2)

In Problems 9-16, find the equation of the line with slope m through the point P.

9          m = 2, P(3,3)                             

10          m = 3, P(-2, 1)

11          m = -½ P(1,-4)                       

12          m=-1, P(2, 4)

13          m = 5, P(0,0)                             

14          m=-2, P(0, 0)

15          m = 0, P(7, 4)                             

16          vertical line, P(4, 5)

In Problems 17-22, a particle moves with constant velocity and has the given positions y at the given times t. Find the velocity and the equation of motion.

17           y = 0 at t = 0,      y = 2 at t = 1

18           y = 3 at t = 0,      y = 1 at t = 2

19           y = 4 at t = 1,      y = 2 at t = 5

20           y = 1 at t = 2,      y = 3 at t = 3

21           y = 4 at f = 0,      y = 4 at t = 1

22           y = 1 at f = 3,     y= -2 at t = 6

23           A particle moves with constant velocity 3, and at time t = 2 is at the point y = 8. Find the equation for its motion.

24           A particle moves with constant velocity ¼, and at time t = 0 is at y = 1. Find the equation for its motion.

In Problems 25-30, find the slope of the line with the given equation, and draw the line.

25           3x - 2y + 5 = 0 

26           x + y - 1 = 0

27           2x-y = 0 

28           6x + 2y = 0

29           3x + 4y = 6 

30           -2x + 4y = -1

31            Show that the line that crosses the x-axis at a ≠ 0 and the y-axis at b ≠ 0 has the equation (x/a) + (y/b) —1 = 0.

32           What is the equation of the line through the origin with slope ml

33           Find the points at which the line ax + by + c = 0 crosses the x- and y-axes. (Assume that a ≠ 0 and b ≠ 0.)

34           Let C denote Celsius temperature and F Fahrenheit temperature. Thus, C = 0 and F = 32 at the freezing point of water, while C = 100 and F = 212 at the boiling point of water. Use the two-point formula to find the linear equation relating C and F.


Last Update: 2006-11-25