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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.
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