# TOPIC 1: COORDINATE GEOMETRY ~ MATHEMATICS FORM 4 ### TOPIC 1: COORDINATE GEOMETRY ~ MATHEMATICS FORM 4

Equation of a Line

The General Equation of a Straight Line

Derive the general equation of a straight line

#### COORDINATES OF A POINT

•The coordinates of a points – are the values of x and y enclosed by the brackets which are used to describe the position of point in a line in the plane.

The plane is called xy-plane and it has two axis.

1. horizontal axis known as axis and
2. vertical axis known as axis
Consider the xy-plane below
The coordinates of points A, B, C ,D and E are A(2, 3), B(4, 4), C(-3, -1), D(2, -4) and E(1, 0).
Definition Example 1
Find the gradient of the lines joining Example 2
(a) The line joining (2, -3) and (k, 5) has a gradient -2. Find k  Exercise 1
1. Find the gradientof the line which passes through the following points ;
1. (3,6) and (-2,8)
2. (0,6) and (99,-12)
3. (4,5)and (5,4)

2. A line passes through (3, a) and (4, -2), what is the value of a if the slope of the line is 4?

3. The gradient of the linewhich goes through (4,3) and (-5,k) is 2. Find the value of k.

#### FINDING THE EQUATION OF A STRAIGHT LINE

The equation of a straight line can be determined if one of the following is given:- Example 3
Find the equation of the line with the following
1. Gradient 2 and intercept
2. Gradient and passing through the point
3. Passing through the points and
Solution  #### EQUATION OF A STRAIGHT LINE IN DIFFERENT FORMS

The equation of a line can be expressed in two forms Example 4
Find the gradient of the following lines  #### INTERCEPTS Therefore Example 5
Find the y-intercept of the following lines Example 6
Find the x and y-intercept of the following lines  Exercise 2
##### Attempt the following Questions.

Find the y-intercept of the line 3x+2y = 18 .

What is the x-intercept of the line passing through (3,3) and (-4,9)?

Calculate the slope of the line given by the equation x-3y= 9

Find the equation of the straight line with a slope -4 and passing through the point (0,0).

Find the equation of the straight line with y-intercept 5 and passing through the point (-4,8).

##### GRAPHS OF STRAIGHT LINES
The graph of straight line can be drawn by using the following methods;
1. By using intercepts
2. By using the table of values
Example 7
Sketch the graph of Y = 2X – 1  #### SOLVING SIMULTANEOUS EQUATION BY GRAPHICAL METHOD

Use the intercepts to plot the straight lines of the simultaneous equations

The point where the two lines cross each other is the solution to the simultaneous equations

Example 8
Solve the following simultaneous equations by graphical method #### Exercise 3

1. Draw the line 4x-2y=7 and 3x+y=7 on the same axis and hence determine their intersection point

2. Find the solutionfor each pair the following simultaneous equations by graphical method;
1. y-x = 3 and 2x+y = 9
2. 3x- 4y=-1 and x+y = 2
3. x = 8 and 2x-3y = 10

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