Linear Equations Coordinate Planemsubmathing.weebly.com/uploads/3/8/0/6/38068469/... · Parallel...
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Linear Equations
Definitions
Coordinate Plane: Two number lines drawn perpendicular to each other.
Quadrants: The four regions defined by the boundaries create by the number lines forming a coordinate plane.
X-Axis: The Horizontal number line in a coordinate plane.
Y-Axis: The Vertical number line in a coordinate plane.
Ordered Pair: The location of a point on a coordinate plane written as (x, y), the x-coordinate and the y-coordinate.
The Origin: The point where the two number lines meet in forming a coordinate plane having the location of the ordered pair (0, 0)
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Examples
Quadrant IQuadrant II
Quadrant III Quadrant IV
A
B
C
D
Find the locations for points A, B, C, and D.
A(-2, 3) B(-3, -3)
C(3, -2) D(4, 5)
Linear Equations
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Definitions
Slope: The ratio in change in the Y direction to the change in the X direction between two points on a line segment. Also known as, the ratio of rise over run.
scoordinate-in x changescoordinate-yin change
runrise
m ¸¹·
¨©§
¸¹·
¨©§
Formulas
Slope of a Line: given two
points on a line (x1, y1) and (x2, y2).
,)1x2(x)1y2(y
m��
Slope of a Horizontal Line: A horizontal line containing point (a, b) is described by the equation y = b and has a slope of 0.
Slope of a Vertical Line: A vertical line containing point (c, d) is described by the equation x = c and has an undefined slope.
Linear Equations
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A
B
Example
Find the slope of .AB
Linear Equations
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Exercises
A
B
C
D
E
FGH
Find the slopes of the following lines.
AB1) 2)
3) 4)
CD
EF GH
Linear Equations
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Examples
Find the slope of the line that passes through points (1, -1) and (-3, -1).
Find the slope of the line that passes through points (-2, 3) and (4, 0).
Linear Equations
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On Your Own
Find the slope of the line passing through the sets of points given below.
1) A(2, 3) and B(8, 6)
2) C(-4, -3) and D(-8, 6)
3) E(2, 2) and F(2, -1)
Linear Equations
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Parallel and Perpendicular LinesDefinitions
Perpendicular: Lines intersecting to form a right or 90o angle.
Reciprocal: The reciprocal of a fraction is the fraction where the numerator and denominator are switched.
Parallel Lines:
If two lines are parallel, they have the same slope.
If two distinct lines have the same slope, they are parallel.
Perpendicular Lines:
If two lines are perpendicular, the product of their slopes is -1. The slopes are negative reciprocals of each other.
If the slopes of two lines are negative reciprocals of each other, the line are perpendicular.
Linear Equations
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Parallel and Perpendicular LinesExamples
Linear Equations
1) Find the negative reciprocal of 4
2) Find the negative reciprocal of 78
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Exercises
Linear Equations
Determine if the lines going through the given point are parallel, perpendicular or neither.
1) The line through points (-5, -3) and (5, 3) and the line through points (7, 9) and (-3, 3).
2) The line through points (6, 5) and (12, 3) and the line through points (0, 2) and (4, -2).
3) The line through points (5, 1) and (1, 9) and the line through points (8, 7) and (-3, 29)