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