Explanation Formula used: The equations x = x 0 + a t , y = y 0 + b t , for − ∞ < t < ∞ , where x 0 , y 0 , a and b with a ≠ 0 , describe a line with slope b a passing through the point ( x 0 , y 0 ) . If a = 0 and b ≠ 0 , the line is vertical. Calculation: The starting and ending point of the line segment is ( 0 , 0 ) to ( 6 , 6 ) . Then, the slope of the line will be, Slope = 0 − 6 0 − 6 = 6 6 = 1 Notice that, when the line segment is traversed from ( 0 , 0 ) to ( 6 , 6 ) , both x and y are increasing. So, b = 1 and a = 1 . The starting point of the line segment is ( 0 , 0 ) . Then, x 0 = 0 and y 0 = 0 . The general form of equation is x = x 0 + a t , y = y 0 + b t . That is, x = t , y = t . Notice that, t = 0 corresponds to the starting point ( 0 , 0 ) . Since the equation represents a line segment, the interval for t must be restricted. Now, the value of t corresponding to the end point of the line segment has to be found out. From the end point ( 6 , 6 ) , x = 6 and y = 6 . Since x = t , y = t , the value of t at the end point is, t = 6 . Therefore, one of the parametric equations for the line segment that goes from ( 0 , 0 ) to ( 6 , 6 ) is x = t , y = t for 0 ≤ t ≤ 6

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 12.1, Problem 9E

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The three different pairs of parametric equations for the line segment that starts at (0,0) and ends at (6,6).

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Chapter 12.1, Problem 8E

Chapter 12.1, Problem 10E

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Chapter 12 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QC Ch. 12.1 - Prob. 3QC Ch. 12.1 - Prob. 4QC Ch. 12.1 - Prob. 5QC Ch. 12.1 - Prob. 6QC Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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The three different pairs of parametric equations for the line segment that starts at ( 0 , 0 ) and ends at ( 6 , 6 ) .

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