coordinates and graphs year 9. note 1: coordinates coordinates require 2 references: 1.) horizontal...
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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
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
Note 1: Coordinates and Maps
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)
Note 1: Mathematical Coordinates
The horizontal scale is the x-axisThe vertical scale is the y-axis (x,y)
Note 1: Mathematical Coordinates
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
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
Note 3: Latitude & Longitude
Note 3: Latitude & Longitude
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
Note 4: Two-dimensional graphsScatter Plots
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)
Note 4: Two-dimensional graphsScatter Plots
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
Note 4: Two-dimensional graphsScatter Plots
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
Note 4: Two-dimensional graphsLine Graphs
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.
Note 4: Two-dimensional graphsLine Graphs
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
Note 6: Connecting tables, rules & graphs
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
Note 6: Connecting tables, rules & graphs
$ 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