Parametric Equations and Linear Functions

The video tutorial explains how to convert parametric equations into a rectangular equation by eliminating the parameter T. It begins with rewriting the given parametric equations, then solving one equation for T and substituting it into the other. The process involves simplifying the equation to achieve the form y = mx + b. The final Cartesian equation is verified by checking the slope and y-intercept on a graph.

What is the main goal when converting parametric equations to a rectangular form?

• To express the equations in terms of x and y

• To eliminate the variable x

• To solve for y in terms of T

• To find the value of T

What are the given parametric equations in the problem?

• x = 5 + T and y = 8 + 3T

• x = 8 + T and y = 5 + 3T

• x = 3T + 5 and y = 8T + 3

• x = T + 8 and y = 5 + 3T

How do you solve for T in the equation x = 5 + T?

• Divide both sides by 5

• Add 5 to both sides

• Multiply both sides by 5

• Subtract 5 from both sides

After substituting x - 5 for T in the second equation, what is the new equation?

• y = 8 + 3(x + 5)

• y = 8 + 3(x - 5)

• y = 8 - 3(x - 5)

• y = 8 - 3(x + 5)

What is the simplified form of the equation y = 8 + 3(x - 5)?

• y = 3x - 7

• y = 3x + 7

• y = 3x - 15

• y = 3x + 15

What is the y-intercept of the line represented by the equation y = 3x - 7?

• 3

• -7

• -3

• 7

What is the slope of the line represented by the equation y = 3x - 7?

• 3

• 4

• 1

• 2

How can you verify that the equation y = 3x - 7 is correct?

• By graphing the line and checking the slope and y-intercept

• By checking the x-intercept

• By solving for x

• By substituting y back into the parametric equations