Assigned work: pg. 433 #1-12 Equation of a line – slope and point or two points BUT NOW we will learn to describe an Equation of a Line by using vectors…………………..

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Presentation transcript:

Assigned work: pg. 433 #1-12 Equation of a line – slope and point or two points BUT NOW we will learn to describe an Equation of a Line by using vectors…………………..

8.1 Parametric & Vector Equations of Line in a Plane Vector Equation of a Line in a Plane: OR

8.1 Parametric & Vector Equations of Line in a Plane The vectors and variables from the previous slide are defined below:

8.1 Parametric & Vector Equations of Line in a Plane Note: A direction vector can give the magnitude of the slope of a line Any parallel vector to a line has a direction vector that is the same or scalar multiple of the direction vector in the given line.

8.1 Parametric & Vector Equations of Line in a Plane Ex1: a) Find the vector equation of the line that passes through points A(3,4) and B(7,2). b) What is the slope of the line?

8.1 Parametric & Vector Equations of Line in a Plane c) Determine a different point on the line. (just choose any value for t …) When t = 1: Therefore:

8.1 Parametric & Vector Equations of Line in a Plane This vector equation can be used to describe a line in terms of its components. An equation written in terms of its components is called the…… “Parametric Equation of a Line”

8.1 Parametric & Vector Equations of Line in a Plane Ex2: A line passes through the point P(-1,1) and has a direction vector a) State the parametric equation of the line.

8.1 Parametric & Vector Equations of Line in a Plane Ex2: b) Does the point (-4,1) lie on the line? (*****if it does (-4,1) will produce the same parameter for both components) Check: Since parameter is NOT the same for both components, the point DOES NOT lie on the line.

8.1 Parametric & Vector Equations of Line in a Plane Ex2: c) Determine the y-intercept of the line. y int (x=0)

8.1 Parametric & Vector Equations of Line in a Plane Parametric equations of a line can be used to find a third form of an equation called “Symmetric Equation of a Line in a Plane” It eliminates the parameter from the parametric equations

8.1 Parametric & Vector Equations of Line in a Plane Ex 3: Find the symmetric equation of the line Therefore the symmetric equation is: