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Equation of a line
0 54321
1
2
3
4
5
-1
-4
-5
-5
-3
-4
-2
-3-1
-2
First we looked at coordinates on a grid
0 54321
1
2
3
4
5
-1
-4
-5
-5
-3
-4
-2
-3-1
-2
Now we will look at lines on a grid
The Equation of the Line
= The Y-intercept
= The gradient of the line= A point on the X-axis
= A point on the Y-axis
The alternative equation
The original Equation of the Line:
The Gradient
The gradient or slope The gradient of a line measures
how steep it is. Here, line A is steeper than line
B, which in turn is steeper than line C.
This means that line A has the biggest gradient, followed by line B, and then C.
To calculate the gradient of a line we select any 2 points on the line and find the rise and the run.
Rise Over Run
The rise is how much the line goes up.
The run is how much the line goes across.
RUN
RISE
A line goes up if and only if its gradient is positive.
A line goes down when its gradient is negative.
A line is horizontal if its gradient is zero.
A line has an undefined gradient if is a vertical line.
Practice Questions
The gradient of this line is:
0Undefined1-1
The gradient of the above line =
The gradient of the above line is equal
to 1
33
Rise
Run= 1
The gradient of the above line =
42
Rise
Run= 2
The gradient of the above line is
equal to 2
The gradient of the above line =
- 42
Rise
Run= -2
The gradient of the above line is
equal to -2
Practice Questions
The Gradient of this line is:
-2 -1/2 2 1/2
We can also work out the gradient of a
line if we know two points on that
line
Equation of the slope
If you want to work out the “slope” or gradient of the line from a set of coordinates you can use this formula:
m = y2 – y1
x2 – x1 The gradient
The Rise
The Run
Example: Find the gradient from the points (–2, 4) and (1, 2). Select a set of points to be the FIRST SET and the Other SECOND
SET
THEN use the equation to solve the gradient:
(–2, 4) and (1, 2). X2, Y2
X1, Y1
Useful Links
http://www.youtube.com/watch?v=O8fo4H_185g
http://www.math-magic.com/algebra/slope.htm
Plotting Lines: Gradient and Y-Intercept
The Y-intercept is the point where the line
crosses the Y axis
The Y-intercept is the point where the line
crosses the Y axis
Step One: Draw the point of the y-intercept.
Step Two: Use the slope to draw the next point.
Step Three: Connect the Points.
m = 23
Example:
Example Two: Lets try to draw a graph for the line:
Y = 2X + 1The 2 in front of the
X represents the Gradient. It can be
represented as:
21
Rise
Run
The value of C or the Y-intercept
is: + 1Therefore the Y-intercept point is
(0, 1)
We can now plot our Graph
Y-Intercept
Gradient or Slope of line:
Our Information:
Y = 2X + 1
Y-Intercept
Gradient or Slope of line:
Our Information:
Y = 6 – 2x
Y = – 2x + 6
Y-Intercept: As there is no C value the intercept will
be
(0,0)
Gradient or Slope of line:
Our Information:
Y = 4x
Equation of The Line Applets
http://www.mathwarehouse.com/algebra/linear_equation/interactive-slope.php
http://www.mathsisfun.com/data/straight_line_graph.html
http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm