coordinates and linear equations miss hudson’s maths
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Coordinates and Linear Equations
Miss Hudson’s Maths
E (1 , -2)
A (4 , 2)
B (0 , 2)
C (-3 , 1)
D (-1 , 0)21
1 2-1-1
-2
-2
1st quadrant2nd quadrant
3rd quadrant 4th quadrant
The point (0,0) is called the origin
Plotting Points
Remember: Across ( ) and then up/down ( )
Miss Hudson’s Maths
Drawing Straight Line Graphs
eg 1: y = x + 2x y-2-1 0 1 2 3
012345
.
.
. . .
Method A: Rostering
5
4
3
2
1
-1
-2
-3
-3 -2 -1 0 1 2 3
Miss Hudson’s Maths
Gradient (Slope)
The gradient tells us how steep a line is.
run
riseGradient
The gradient of line AB = 3
2
The gradient of line BC = 4
1
2
3
rise
run
-1
4
Miss Hudson’s Maths
A line sloping this way: has a positive gradient
A line sloping this way: has a negative gradient
Two special cases:
A horizontal line has gradient = 0
rise = 0
A vertical line has gradient = undefined
run = 0
gradient =numbera
0
= 0
gradient =0
numbera
we can’t divide by zeroMiss Hudson’s Maths
Drawing Straight Line Graphs
x
y
eg 1: Draw the line y = 23
1x
x
y 1. Mark 2 on the y-axis
2. Step off the gradient a couple of times
x1
3 13
3. Draw the line - long
y-intercept =gradient =
23
1
Method B: Gradient – Intercept Method
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
4
3
2
1
-1
-2
-3
The general equation for a straight line is y = mx + c where m is the gradient and c is the y-intercept.
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eg 2: Draw the line y = -2x + 1
x
y
x
y
1. Mark 1 on the y axis
2. Step off the gradient a couple of times
x
1
-2
y-intercept =gradient = 1-2
1
2
-2
1
3. Draw the line - long Rememberthe gradient
is
run
rise
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
4
3
2
1
-1
-2
-3
-4
Miss Hudson’s Maths
Horizontal & Vertical Lines
A horizontal line has an equation of the form y = a number
eg y = 3 is a line parallel to the x-axis passing through 3
1 2
3
45
1
2
3 4 5-1
-1-2
-2
-3
-3-4
-4
-5
-5
0
y = 3
A vertical line has an equation of the form x = a number
eg x = -2 is a line parallel to the y-axis passing through -2
x = -2
Miss Hudson’s Maths
Remember:
The general equation for a straight line is y = mx + c where m is the gradient and c is the y-intercept.
The equation of this graph would be written as:
y = mx + c13
21 2 3 4 5 6
5
4
3
2
1
Miss Hudson’s Maths