1. COORDINATE GEOMETRY In this chapter we will be learning to: oFind the equation of a line from geometrical information oFind the general equation of a line using points and gradients oDetermine if two lines are parallel or perpendicular

2. COORDINATE GEOMETRY PRE-KNOWLEDGE Before starting this chapter you should be able to: oRecognise a linear equationRecognise a linear equation oPlot a straight line graphPlot a straight line graph oIdentify the gradient and the y-intercept from the equation of a straight line.gradient and the y-intercept oFind the points of intersection of a line and the co-ordinate axes.points of intersection

3. COORDINATE GEOMETRY Week Commencing Monday 26 th October Learning Intention: 1.To be able to find the equation of a line given the gradient and the y-intercept 2.To be able to find the gradient of a line given two points on the line. Contents: 1.Equations of Straight LinesEquations of Straight Lines 2.Finding the Gradient of a Line Given 2 Points on the LineFinding the Gradient of a Line Given 2 Points on the Line 3.Assignment 1Assignment 1 4.Pre-Knowledge RevisionPre-Knowledge Revision

4. COORDINATE GEOMETRY STRAIGHT LINES The equation of a straight line generally takes two forms: (i)ax + by + c = 0 where a, b and c are integers or (ii)y = mx + c where m is the gradient and c is the y-intercept

5. COORDINATE GEOMETRY STRAIGHT LINES If an equation is written in the form ax + by + c = 0 it can be rearranged into the form y = mx + c so that the gradient and the y-intercept can be easily read. Example: Write 2x + 3y + 5 = 0 in the form y = mx + c and state the gradient and y-intercept of the line. Solution: Taking the x term and the number to the RHS gives: by dividing across by 3 Gradient = -2/3 and y-intercept = -5/3

6. COORDINATE GEOMETRY STRAIGHT LINES If we know the gradient of a line and its y-intercept we can write the equation of the line. Example: A line is parallel to the line y = 1/3x – 4 and crosses the y- axis at the point (0, 6). Write down the equation of the line. Solution: As the line is parallel to y = 1/3x – 4 the gradient we need is 1/3. As the point (0, 6) is on the y-axis the y-intercept = 6. So, equation of the required line is: y = 1/3x + 6

7. COORDINATE GEOMETRY STRAIGHT LINES Example: A line is parallel to the line 3x + 5y + 1 = 0 and it passes through the point (0, 4). Work out the equation of the line. Solution: To find the equation of the line we need the gradient and the y-intercept. We have the y-intercept from the point: 4. To find the gradient we need to re-arrange the equation of the given line. This gives: 5y = -3x – 1 y = -3/5x – 1/5 therefore required gradient = -3/5 Equation of required line is: y = -3/5x + 4

8. COORDINATE GEOMETRY FINDING THE GRADIENT WHEN GIVEN 2 POINTS If given two points on a line, (x 1, y 1 ) and (x 2, y 2 ), we can find the gradient of the line using the formula:

9. COORDINATE GEOMETRY FINDING THE GRADIENT WHEN GIVEN 2 POINTS Example: Work out the gradient of the line joining the points (3, 4) and (5, 6). Solution: We can use the formula (3, 4) gives x 1 = 3y 1 = 4 (5, 6) gives x 2 = 5y 2 = 6 Substituting into the formula we get:

10. COORDINATE GEOMETRY FINDING THE GRADIENT WHEN GIVEN 2 POINTS Example: The line joining (2, -5) to (4, a) has gradient -1. Work out the value of a. Solution: Substituting into the formula for the gradient we get:

11. COORDINATE GEOMETRY Assignment 1 Follow the link for Assignment 1 in the Moodle Course Area underneath Coordinate Geometry. This is a Yacapaca Activity. Assignment must be completed by 5:00pm on Wednesday 4 th November 2009

12. COORDINATE GEOMETRY PRE-KNOWLEDGE REVISION

13. COORDINATE GEOMETRY Linear Equations A linear equation is an equation that DOES NOT contain any powers higher than 1. Example: 3x + 2y = 1 is a linear equation 3x 2 + 2y = 1 is NOT a linear equation as it contains x 2

14. COORDINATE GEOMETRY Plotting a Straight Line Graph To plot a straight line graph: 1.Make a table of values for at least three values of x. 2.Find the corresponding values of y 3.Plot the points found 4.Join points with a straight line

15. COORDINATE GEOMETRY Identifying Gradient and y-intercept If the equation of a line is given as y = mx + c, the coefficient of x is the gradient c is the y-intercept (the point where it crosses the y-axis)

16. COORDINATE GEOMETRY Points of Intersection of Lines and Coordinate Axes To find where a line cuts the x-axis let the equation equal 0. To find where a line cuts the y-axis let x equal 0 in the equation.