Review of the line Representations of a line

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Review of the line Representations of a line: • Graphically • Rule(equation) Y= ax+b

Review of the line Representations of a line: • Graphically • Rule(equation) Y= ax+b • Any two ordered pairs on a Cartesian plane (x 1, y 1) and (x 2, y 2) • A point and slope • Table of values

Rule (equation) of line in standard form Y = ax+b • a and b

Rule (equation) of line in standard form Y = ax+b • a and b represents the parameters that determine the orientation of the line. X and y are the variables. • a: • b:

Finding the rule from a graph Given any two points on a line, you

Finding the rule from a graph Given any two points on a line, you can find the equation of that line.

Examples

Examples

Graphing a line from a rule • Given the rule y=2 x-6, graph this

Graphing a line from a rule • Given the rule y=2 x-6, graph this line.

Graphing a line from a rule • Given the rule y=-4 x+5, graph this

Graphing a line from a rule • Given the rule y=-4 x+5, graph this line.

Different forms of the rule of the line

Different forms of the rule of the line

Role of parameters a and b • Parameter a: • Parameter b:

Role of parameters a and b • Parameter a: • Parameter b:

Special lines • Vertical (parallel to the yaxis) • Horizontal (parallel to the x

Special lines • Vertical (parallel to the yaxis) • Horizontal (parallel to the x -axis) Equation:

Examples • Find the equation of a line passing through (6, -9) and (4,

Examples • Find the equation of a line passing through (6, -9) and (4, 11). • Find the equation of the line whose y-intercept is -2 and whose x-intercept is 9 (in general form).

Examples • Find the equation of a line with a slope of ½ and

Examples • Find the equation of a line with a slope of ½ and passing through the point (8, 3). • Find the equation of a line with a x-intercept of 4 and passing through the point (9, 10).

Relationships between lines • Intersecting lines: Any two lines who share only one common

Relationships between lines • Intersecting lines: Any two lines who share only one common point. We call this the point of intersection (POI). What does this mean for their slopes? Initial value?

Special relationships between lines • Perpendicular lines: lines that intersect at a right (90

Special relationships between lines • Perpendicular lines: lines that intersect at a right (90 degree) angle.

Special relationships between lines • Parallel lines: Lines that follow the same direction. Never

Special relationships between lines • Parallel lines: Lines that follow the same direction. Never meet (intersect)

Special relationship between lines • Coincident lines: lines which fall on the exact same

Special relationship between lines • Coincident lines: lines which fall on the exact same path (i. e. same line).

Determine the relationships between these lines 1. LI: Y=2 x-7 and L 2: 2

Determine the relationships between these lines 1. LI: Y=2 x-7 and L 2: 2 y-4 x+6 2. LI: passing through (3, 7) and (6, 6) L 2: slope of -3 and an x-intercept of 9

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