Understanding Parametric Equations

The video tutorial explains how to derive parametric equations for a line segment between two points. It starts by introducing the concept of parametric equations and their orientation. The tutorial then walks through the process of determining the parameters a, b, c, and d by using initial and final conditions. The final parametric equations are formulated, and the linear nature of these equations is discussed. The tutorial concludes with a summary of the key points.

What is the form of the parametric equations for a line segment?

• x = at + b and y = ct + d

• x = a - bt and y = c - dt

• x = ab + t and y = cd + t

• x = a + bt and y = c + dt

If the segment starts at (8, 5) when t=0, what must be the value of 'a'?

• 0

• 5

• 8

• 2

What is the value of 'c' if y(0) must equal 5?

• 0

• 8

• 2

• 5

How do you find the value of 'b' given x(1) must equal 2?

• Add 8 to 2

• Multiply 8 by 2

• Subtract 8 from 2

• Divide 8 by 2

What is the value of 'd' if y(1) must equal 1?

• -6

• 6

• 4

• -4

What is the parametric equation for x(t) after finding 'a' and 'b'?

• x(t) = 6 + 8t

• x(t) = 8 + 6t

• x(t) = 8 - 6t

• x(t) = 6 - 8t

What is the parametric equation for y(t) after finding 'c' and 'd'?

• y(t) = 4 - 5t

• y(t) = 5 + 4t

• y(t) = 5 - 4t

• y(t) = 4 + 5t

What does the slope 'b' represent in the parametric equation for x?

• Change of y with respect to x

• Change of t with respect to x

• Change of y with respect to t

• Change of x with respect to t

How can you calculate 'b' using the change in x and t?

• Add the change in x to the change in t

• Multiply the change in x by the change in t

• Divide the change in x by the change in t

• Divide the change in x by the change in y

What is the change in y divided by the change in t for 'd'?

• -6

• 5

• -4

• 1