1. Equation of a line

2. First we looked at coordinates on a grid5 4 x 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5

3. Now we will look at lines on a grid5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5

4. The Equation of the LineY X + c m = X m
= A point on the X-axis
= The gradient of the line Y c
= A point on the Y-axis
= The Y-intercept

5. The alternative equationor X = Y -c m Y = X m c +
The original Equation of the Line:

6. The Gradient

7. 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.

8. Rise Over Run RISE RUN The rise is how much the line goes up.
The run is how much the line goes across.
RISE
RUN

9. A line goes up if and only if its gradient is positive.

10. A line goes down when its gradient is negative.

11. A line is horizontal if its gradient is zero.

12. A line has an undefined gradient if is a vertical line.

13. Practice Questions
The gradient of this line is:
Undefined 1 -1

14. Practice Questions 3 4 2 - 4 2 1 -2 = = =
The gradient of the above line =
The gradient of the above line =
The gradient of the above line = 3
Rise
Run = 1 4 2
Rise
Run =
- 4 2
Rise
Run = -2
The gradient of the above line is equal to 1
The gradient of the above line is equal to 2
The gradient of the above line is equal to -2

15. The Gradient of this line is:-2
-1/2 2
1/2

16. We can also work out the gradient of a line if we know
two points on that line

17. y2 – y1 x2 – x1 m = 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:
y2 – y1
x2 – x1
The Rise
m =
The Run
The gradient

18. 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
X1, Y1
X2, Y2
(–2, 4) and (1, 2).
THEN use the equation to solve the gradient:

19. Useful Links http://www.youtube.com/watch?v=O8fo4H_185g

20. Plotting Lines: Gradient and Y-Intercept

22. The Y-intercept is the point where the line crosses the Y axis

23. Example: 2 3 m = 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 = 2 3

24. Y = 2X + 1 We can now plot our Graph Example Two: 2 1 Y = X m c +
Lets try to draw a graph for the line:
Y = 2X + 1
The value of C or the Y-intercept is: + 1
Therefore the Y-intercept point is
(0, 1)
The 2 in front of the X represents the Gradient. It can be represented as: 2 1
Rise
Run
We can now plot our Graph

25. Gradient or Slope of line:
Y = 2X + 1
Our Information:
Gradient or Slope of line:
Y-Intercept

26. Gradient or Slope of line:
Y = 6 – 2x
Y = – 2x + 6
Our Information:
Gradient or Slope of line:
Y-Intercept

27. Y = 4x (0,0) Our Information: Gradient or Slope of line: Y-Intercept:
As there is no C value the intercept will be
(0,0)

28. Equation of The Line Applets