1. COORDINATE GEOMETRY Week commencing Monday 2nd November 2009
Learning Intention:
Given a point and the gradient to be able to find the equation of a line.
Contents:
1. Equation of a Straight Line from gradient and a point
2. Examples
3. Assignment 2 1

2. EQUATION OF A LINE FROM POINT & GRADIENT
COORDINATE GEOMETRY
EQUATION OF A LINE FROM POINT & GRADIENT
If given the gradient of a line and a point, (x1, y1), on the line we can find the equation of line using the formula:
y – y1 = m(x – x1) 2

3. EQUATION OF A LINE FROM POINT & GRADIENT
COORDINATE GEOMETRY
EQUATION OF A LINE FROM POINT & GRADIENT
Example:
Find the equation of the line with gradient 4 that passes through the point (1, 3).
Solution:
m = 4 (x1, y1) = (1, 3)
Substituting into formula we get:
y – 3 = 4(x – 1)
y – 3 = 4x – 4 expanding brackets
y = 4x – simplifying
y = 4x – 1 in form y = mx + c 3

4. EQUATION OF A LINE FROM POINT & GRADIENT
COORDINATE GEOMETRY
EQUATION OF A LINE FROM POINT & GRADIENT
Example:
Find the equation of the line with gradient -½ that passes through the point (5, 3).
Solution:
m = -½ (x1, y1) = (5, 3)
Substituting into the formula we get: 4

5. EQUATION OF A LINE FROM POINT & GRADIENT
COORDINATE GEOMETRY
EQUATION OF A LINE FROM POINT & GRADIENT
Example:
The line y = 4x – 8 meets the x-axis at the point A. Find the equation of the line with gradient 3 that passes through the point A.
Solution:
We first need a point on the required line. We can get this by finding the coordinates of A.
Let y = 0 to find where y = 4x – 8 meets the x –axis.
4x – 8 = 0
4x = 8
x = 2 coordinates of A are (2, 0)
m = 3 (2, 0) Substitute into formula
y – 0 = 3(x – 2)
y = 3x - 6 5

6. COORDINATE GEOMETRY Assignment 2
Follow the link for Assignment 2 in the Moodle Course Area underneath Coordinate Geometry. This is a Yacapaca Activity.
Assignments to be completed by 5:00pm on Monday 9th November 2009 6