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