Ordered Pairs and the Coordinate Graph Cartesian Plane.
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Transcript of Ordered Pairs and the Coordinate Graph Cartesian Plane.
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Ordered Pairs and the Ordered Pairs and the Coordinate GraphCoordinate Graph
Ordered Pairs and the Ordered Pairs and the Coordinate GraphCoordinate Graph
Cartesian PlaneCartesian Plane
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The Cartesian Coordinate Plane
The Cartesian plane was the brainchild of French mathematician Rene Descartes trying to combine algebra and geometry together.
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To explain Descartes method, first think of using a map. If you are trying to find a
specific location you use reference points around the outside of the map and trace
down and across to find your location. It’s like using longitude and latitude.
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You learned about basic (counting) number lines back in elementary school.
Later on, you were introduced to zero and negatives, which completed the number
line.Descartes took a second number line and
standing it on end, crossed the lines at zero to form a grid like pattern.
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The number lines when drawn like this, are called “axes”. The horizontal line is called the “x-axis”; the vertical line is called the
“y-axis”.By the way, the arrows at the ends of the axes indicate the direction in which the
numbers are getting larger.
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Each coordinate plane is divided into
quadrants. Using the “ordered pairs” or the x- and y-axes you can find a point
on the plane.
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To plot an ordered pair, begin at the origin, the
point (0, 0), which is the intersection of the x-
axis and y-axis.The first coordinate tells
how many units to move left or right; the second coordinate tells
how many units to move up and down.
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X-coordinate move right or left
y-coordinate move up or down
(x, y)The sign of the
number indicates which direction to
move.Positive: up or right
Negative: down or left
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order pairs – a pair of numbers used to locate a point on a coordinate plane.coordinate plane – a plane formed by the intersection of a horizontal number line called the x-axis and a vertical line called the y-axis.x-axis – the horizontal axis on a coordinate plane.y-axis – the vertical axis on a coordinate plane.x-coordinate – the first number in an ordered pair; it tells the units to move right or left from the origin.y-coordinate – the second number in an ordered pair; it tells the units to move up or down from the origin.
More definitions
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origin – the point where the x-axis and the y-axis intersect on the coordinate plane.graph of an equation – the set of all ordered pairs that are solutions of the equation.dependent variable – the y-coordinate of an equation, which depends on what the x-value will be. (in the equation y = 2x, the y-value depends on what the value of x is.)independent variable – the x-coordinate of an equation, which when substituted will determine what the y-value will be. (in the equation y = 2x, the value of x will determine what the value of y equals)
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Draw this coordinate plane on graph paper and
label all parts.
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Graphing an EquationGraphing an EquationGraphing an EquationGraphing an Equation
Using ordered pairsUsing ordered pairs
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The good, the bad and the ugly. When graphing you always use graph
paper and draw neatly.NO HAND DRAWN GRAPHS
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Complete the table of values to determine the ordered pairs. Graph the equation on a
coordinate plane.
x y = 2x + 3 y (x, y) -2 -1 0 1 2
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Graph of the equation y = 2x + 3
X Y = 2x + 3 Y (x, y) -2 2(-2) + 3 = -4 + 3 = -1 -1 (-2, -1) -1 2(-1) + 3 = -2 + 3 = 1 1 (-1, 1) 0 2(0) + 3 = 0 + 3 = 3 3 (0, 3) 1 2(1) + 3 = 2 + 3 = 5 5 (1, 5) 2 2(2) + 3 = 4 + 3 = 7 2 (2, 7)
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Make a table of values for the following equations and graph each on the coordinate graph.
y = x + 1 y = 3x y = 2x - 1
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Cartography, the science of map making, is an application of graphing on a coordinate plane. Cartographers map a region of the surface of the earth onto part of a plane.