The y- intercept of a line is where the line crosses the y - axis. This can be read directly off the graph.
Level 5 NZ Curriculum Achievement Objectives for Linear and Quadratic Graphs
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA 5-9: Relate tables, graphs, and equations to linear relationships found in number and spatial patterns.
NA 5-9: Relate tables, graphs, and equations to linear relationships found in number and spatial patterns.
In this unit you will revise:
1) Using linear patterns to draw a graph and write and use an equation |
In this unit you will learn:
2) Finding the gradient of a line (m) 3) Finding the y - intercept of a line (c) 4) Write an equation using the gradient and y - intercept (y = mx + c) 5) Graph a line using the gradient and y - intercept |
Homework Book Pages:
On Track 1: Pages 56 - 65 On Track 2: Pages 43 - 55 Fast Track 2: Pages 41 - 54 |
1) Using linear patterns to draw a graph and write and use an equation
- A variable is a letter or a symbol that is used to decribe infinitely many numbers.
- Variables allow us to write expressions that describe all possible sentences for a given situation.
- To find a general rule or a number pattern, decide 'what is the same' and 'what is different'.
- When an equation is written using variables, it is called a rule or a formula e.g. 3 x a - 2 = b or 3 x m - 2 = n
- Mathematicians leave out the x sign between a number and a variable to be more efficient. e.g. 3a - 2 =b
Have a look at these sites:
https://www.mathsisfun.com/algebra/sequences-finding-rule.html
http://www.virtualnerd.com/middle-math/number-algebraic-sense/sequences-patterns/write-pattern-sequence-rule
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FINDING RULES FOR NUMBER PATTERNS FROM A TABLE OF VALUES
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Check out these websites
http://www.mathplanet.com/education/algebra-1/discovering-expressions,-equations-and-functions/representing-functions-as-rules-and-graphs
NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
http://www.mathplanet.com/education/algebra-1/discovering-expressions,-equations-and-functions/representing-functions-as-rules-and-graphs
NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Plotting Coordinates
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2) Finding the Gradient of a Line (m)
The Gradient (also called Slope) of a straight line shows how steep a straight line is.
To calculate the Gradient:
Divide the change in height by the change in horizontal distance
To calculate the Gradient:
Divide the change in height by the change in horizontal distance
We sometimes use the words rise / run to describe gradient as well.
The gradient of this line is 3/3 = 1.
The gradient of this line 4/2 = 2.
The line is steeper so the number is larger.
The line is steeper so the number is larger.
The gradient of this line is 3/5.
The line is less steep so the number is smaller.
The line is less steep so the number is smaller.
Horizontal Lines
All lines that go straight across have no rise. Therefore their gradient = 0. The example below has a rise of 0 and and a run of 5. Therefore the gradient = 0/5 = 0 |
Vertical Lines
All lines that go up and down have no run. Therefore their gradient = undefined. The example below has a rise 3 and a run of 0. Therefore the gradient = undefined. |