Expanded
Syllabus
Chapter 2 : The Rectangular Coordinate System and Graphs of Equations (x, y) |
College
Algebra
by Examples Chapter Summary
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2.1 The Rectangular Coordinate System | Points: P(x1 , y1)
and Q(x2 , y2),
where x1 is the x-coordinates with the smallest
value
Distance between P and Q is given by d:
Midpoint between P and Q is given by the coordinates:
Equation of Vertical line is x =
a
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2.2
Slope of a Nonvertical Line
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Slope of a line is given by formula
For points: P(x1 , y1) and Q(x2 , y2) For 2 lines with slopes : Slope if line is a horizontal line Slope is undefined if line is a vertical line Slope if both lines are parallel Slope if lines are perpendicular |
2.3
Writing Equations of Lines
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General form:
Point-Slope form: Slope-intercept form: |
2.4
Graphs of Equations
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Intercepts:
(a) y-intercept: value of y when x = 0 (b) x-intercept(s); values of x when y = 0 Symmetry: (a) About the y-axis if (b) About the origin is Equation of a Circle: (a) , where center is (0, 0) (b) , where center is (h, k) |
2.5
Proportion and Variation
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Directly Proportional, k
is constant of proportionality
Inversely Proportional:
Joint Proportional:
Combine |