Coordinates and Graphs Year 9. Note 1: Coordinates Coordinates require 2 references: 1.) Horizontal...

Coordinates and GraphsYear 9

Note 1: Coordinates

Coordinates require 2 references:

1.) Horizontal (written first)

2.) Vertical (written second)

Coordinates can be used to identify a place of interest.

Note 1: Coordinates and Maps


Topographical Maps show many features including:

• heights (elevations)• contours• vegetation• water and coastal features• roads, railways, bridges and tunnels• residential and historical landmarks


The caravan park at Orongo Bay has a grid reference 152569

Split the reference into 2 parts

The first 3 digits (152) represent the horizontal scale

The second 3 digits (569) represent the vertical scale

15.2

56.9

Note 1: Mathematical Coordinates

• In math, we use coordinates to represent a position on a whole number plane

The coordinate of point A is _______

The coordinate of point B is _______

(1,3)

(5,2)

* Remember, the first coordinate gives the distance across (horizontal) and the second gives the distance up (vertical)


The horizontal scale is the x-axisThe vertical scale is the y-axis (x,y)


The horizontal scale is the x-axisThe vertical scale is the y-axis (x,y)

4 4

2 1

1 5

0 1

3 0 IWB Ex 16.01 pg 411-412 Ex 16.02 pg 415-416 Ex 16.03 pg 418-419

Note 2: Coordinates with integers

We can extend the x and y axes to include negative numbers

* Remember we always write x before y

(0,0) is the point where the x-axis and the y-axis intersect. This point is called the origin.

(x,y)

Note 2: Coordinates with integers

IWB Ex 16.04 pg 423-424

-1 3

-2 -4

5 -2

3 4

0 -2

Note 3: Latitude & Longitude


Latitude – horizontal lines (run east –west)

Longtitude – vertical lines (run north-south)

e.g. Equator

e.g. Prime Meridian Greenwich, London, England


IWB Ex 16.05 pg 431

Note 4: Two-dimensional graphsScatter Plots

• shows the relationship between the two quantities

• two axes, each with a different quantity and scale


This scatter plot shows the relationship between height and age

1.) Who is the youngest?

2.) Who is the tallest?

3.) If these are all children in a single family, who are the twins?

4.) What is the relationship that this graph shows between height and age?

Cindy

Aaron

Bruce & Emma

The older a person is, the taller they are (positive relationship)


This scatter plot shows the distances of some overseas destinations from Auckland airport, and the cost of the return ticket to each one.

a.) Which destination is the furthest from Auckland?

b.) Which destination is the most expensive to travel to?

c.) How does the graph show that the fare to Sydney and Melbourne is the same?

Seoul

L.A.

They are on the same horizontal lineWith a fare of $500


This scatter plot shows the distances of some overseas destinations from Auckland airport, and the cost of the return ticket to each one.

d.) The distance to Adelaide is 3250 km and the fare is $799, add this to the graph.

e.) What relationship does this graph show exists between distance and cost ?

The further away destinations are more expensive to travel to (positive relationship)

Note 4: Two-dimensional graphsLine Graphs

• Show how one quantity changes as another one does

• two axes, each with a different quantity and scale


This graph shows what happens to two plants after they were planted in a garden. One received fertilizer and the other did not.a.) What was their height when they were planted?

b.) Which plant grew the fastest?

c.) How does the graph show when the plants stop growing?

10 cm

Plant A – it has a steeper slope (gradient)

Plant A stopped after 16 days and plant B after 18 days – their graph becomes horizontal after day 16 & 18.


Sue is adding water to a storage tank with a hose but doesn’t realize that there is a leak in the tank. When the tank looks full, she stops adding water and walks away.

a.) What is the level in the tank when she starts filling it?

b.) How long does it take to fill the tank?

c.) At what level is there a hole in the tank?

0.4 m = ____ cm 40

20 min

0.8 m = ____ cm 80 IWB Ex 17.01 pg 435Ex 17.02 pg 440

Note 5: Graphs & Coordinate PatternsAn algebra rule that links x and y can be used to plot coordinates that produce a pattern on a graph

e.g. y = 2x

x y = 2x-2-10123

2×-2 = -42×-1 = -22 × 0 = 02 × 1 = 22 × 2 = 4

2 × 3 = 6

Coordinates

(-2,-4)(-1,-2)(0 , 0 )(1 , 2 )(2 , 4 )(3 , 6 )

Once the coordinates are plotted the pattern is obvious Linear

Note 5: Graphs & Coordinate PatternsAn algebra rule that links x and y can be used to plot coordinates that produce a pattern on a graph

e.g. y = 3x – 1

x y = 3x – 1 -2-10123

3×-2-1 = -73×-1-1 = -43× 0-1 = -13× 1-1 = 23× 2-1 = 5

3× 3-1 = 8

Coordinates

(-2,-7)(-1,-4)(0 , -1)(1 , 2 )(2 , 5 )(3 , 8 )

Linear Pattern

Note 5: Graphs & Coordinate Patterns

3 × -1 = -33 × 0 = 03 × 1 = 33 × 2 = 63 × 3 = 9

(-1,-3)(0 , 0)(1 , 3 )(2 , 6 )(3 , 9 )

Linear Pattern

IWB Ex 18.01 pg 449-451

Starter

-2 × -1 – 1 = 1-2 × 0 – 1 = -1-2 × 1 – 1 = -3-2 × 2 – 1 = -5-2 × 3 – 1 = -7

(-1, 1)(0 , -1)(1 ,-3 )(2 , -5 )(3 , -7 )

Linear Patterny = -2x -1

-2 × -2 – 1 = 3 (-2, 3)

-2x – 1 = y

Note 6: Connecting Tables, Rules & Graphs

Rule: W = 10 – 2n W = amount of water (L) n = number of minutes elapsed since the bucket was full

1.) What is the value of W when n=1?2.) How much water is left in the bucket after 2 min.?

3.) How much water is in the bucket when it is full?4.) How long does it take to empty the bucket?

8 Litres6 Litres

10 Litres5 minutes

Note 6: Connecting tables, rules & graphs

C = 2n + 30

36 = 2 x 3 + 30

3234

3840


C = 2n + 30

At time 0, the cost is $30. (y-intercept)

When C = $41, n = 5.5 minutes

IWB Ex 18.03 pg 465


$ 0$ 1.5

$ 4.5$ 6.0$ 7.5

Does it make sense to extend the line below the x-axis?

Yes, it shows a loss if they sell less than 4 apples

Note 7: Gradients

The gradient of a line is a number that tells us how steep it is

We measure gradients by describing how much the line rises for every 1 unit of sideways movement

Note 7: Gradients

The gradient of a line is a number that tells us how steep it is

This line has a gradient of 2

We can think of it as the fraction 21

Note 7: GradientsWhat are the gradients of these lines? rise

run

riserun

11

= = 1 =riserun

23

Note 7: Gradientsriserun

11

= 1 13

21 = 2

Note 8: Negative Gradients riserun

-2 1 = -2

14

-1 3

Write down the gradients of these lines

-2 2

= -1BETA Ex 27.6 pg 371Ex 27.7 pg 372

Note 9: y-intercept

The y-intercept of a line is a number that tells us where it crosses the y-axis

y=mx+cy-intercept

gradient

Coordinates and Graphs Year 9. Note 1: Coordinates Coordinates require 2 references: 1.) Horizontal...

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