1.3 the cartesian coordinate system
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1.3 The Cartesian Coordinate System. The Cartesian Coordinate System. y-axis. have ordered pairs Cartesian = coordinate = rectangular system Soooo Review!. Quad I. II. the coordinate plane has coordinate axes (x & y). x-axis. origin. IV. III. - PowerPoint PPT PresentationTRANSCRIPT
1.3 The Cartesian Coordinate System
The Cartesian Coordinate Systemhave ordered pairsCartesian = coordinate = rectangular system
Soooo Review!x-axis
y-axis
origin
Quad III
III IV
the coordinate plane has
coordinate axes (x & y)
*every point has a unique ordered pair (x, y)
abscissa ordinate
*you can create a “graph” by plotting coordinate pairs*remember your axes don’t have to have the same scale – use what works/fits best!
- known pairs can help you estimate new pairs- knowing all pairs can help you estimate/get an equation
(image)(pre-image)
Ex 1) A toaster plant has an automated production line. x represents # of hours per day line functions and y number of toasters.Plot what you know and try to fill in the missing numbers in the chart.
x 15 17 19 21 24
y 1045 1320
maybe 800
maybe 900
maybe1100
1500
1250
1000
750
500
240
2118151293
250
6
(x-int is when y = 0 & y-int is when x = 0)
*Graphing by finding intercepts is a convenient way to graph
Or change graph to y =
Ex 2) A mathematical model turns out to be 16x + y = 2150
(1) x & y-ints
x y
134.3750
02150
OR (2) y = –16x + 2150
2500
2000
1500
1000
500
1400 12010080604020
*We can also utilize our graphing calculator & adjust the window if need be
- Remindery = x
(basic line)
y = x2
(basic parabola)y = x3
(basic cubic)
Use y = ____, can try ZOOM Standard or ZOOM Fit or adjust window manually
Not all eqtns have x’s & y’s!!So how do you know which letter correlates to the x-axis?!?!The letter that correlates to the x-axis is called the independent variable(y is the dependent variable)
5( )
Ex 3) Graph 4 15 5 70q h
(q is the independent variable)
1 45 5 70h q
4 350h q 400
350
300
250
200
1000 80604020
150
Homework
#103 Pg. 21 #1, 6, 9, 11, 13, 15, 18, 19, 21, 23, 27, 29, 32, 36, 45