Coordinate geometry has much to do with points on a graph. But how do you know how to place these points on a graph? This can be done by reading a coordinate table. From the graph constructed, one must know how to to determine the gradient of a line which is the level of incline or decline of a line. Many things can be determined from a slope, for instance, one could determine whether two lines are parallel, perpendicular, solving through a system of equations. Now, we will teach you how to solve the intersection between lines.

INTRODUCTION

We have already known that the equation of a line is y=mx+c. What if we have two lines that intersect with each other? Isn't there something special or strange about the point of intersection? What is it?

Concepts

Before solving the coordinates of simultaneous line equations, we need to consider:

the value of x and y will always be the same at the intersection point of both lines

in other words, the x-value at the point of intersection is the solution that fits both lines

basically, to solve intersection of two lines is to solve two simultaneous linear equations

[Huang Yan, Yi Shun, Darryl]

What are we trying to get when we solve for the coordinates of 2 intersecting lines?

To find the common solution of the lines or the point at which both lines intersect.

Method

1)Find out the equation of the 2 intersecting lines, in the form of y=mx+c.

2)Set the non-y-side part of each equation to equal each other. In other words , you should have:

mx+c (line 1) = mx+c (line 2)

3)Solve for x.

Example

As there is an intersecting point, the value of x in both equation will be the same. For example we have two equations:

y=2x+3 (We shall name this equation 1)

y=0.5x+7 (We shall name this equation 2)

The graph of the equation would be just like this:

We can set 2x+3=0.5x+7 to find the value of x. The value of x will be the same in both equations. With the value of x, we can find the value of y by substituting x in both equations. The answers for y in each equation will be the same.Therefore, after solving the equation, we can find that

[This website teaches you step by step on how to derive the coordinates of intersection between lines. It is quite easy to understand and a suitable resource for students who wants to learn about solving coordinates.]

2) [It tells you about uses of geometry and coordinate geometry.]

BACK TO CHAPTER 5 References: 1) Secrets of scoring Distinction by Kelvin Lee, chapter 10.6: Linear and Quadratic Graphs External Links: 1) Fonts made by http://web2.0write.com/

by

Sebastian Guek

Chong Yi Shun

ChenHuangYan

Darryl Ling Jing Jie

Lee Jia Yi

Gunn Wei Lim

Chia Hou Yi

Lim Wei Hng

Table of Contents## "Recap"

Coordinate geometry has much to do with points on a graph. But how do you know how to place these points on a graph? This can be done by reading a coordinate table. From the graph constructed, one must know how to to determine the gradient of a line which is the level of incline or decline of a line. Many things can be determined from a slope, for instance, one could determine whether two lines are parallel, perpendicular, solving through a system of equations. Now, we will teach you how to solve the intersection between lines.INTRODUCTIONWe have already known that the equation of a line is y=mx+c. What if we have two lines that intersect with each other? Isn't there something special or strange about the point of intersection? What is it?ConceptsBefore solving the coordinates of simultaneous line equations, we need to consider:the value of x and y will always be the same at the intersection point of both linesin other words, the x-value at the point of intersection is the solution that fits both linesbasically, to solve intersection of two lines is to solve two simultaneous linear equations[Huang Yan, Yi Shun, Darryl]What are we trying to get when we solve for the coordinates of 2 intersecting lines?To find the common solution of the lines or the point at which both lines intersect.Method1)Find out the equation of the 2 intersecting lines, in the form of y=mx+c.2)Set the non-y-side part of each equation to equal each other. In other words , you should have:mx+c (line 1) = mx+c (line 2)3)Solve for x.ExampleAs there is an intersecting point, the value of x in both equation will be the same. For example we have two equations:y=2x+3 (We shall name this equation 1)y=0.5x+7 (We shall name this equation 2)The graph of the equation would be just like this:We can set 2x+3=0.5x+7 to find the value of x. The value of x will be the same in both equations. With the value of x, we can find the value of y by substituting xin both equations. The answers for y in each equation will be the same.Therefore, after solving the equation, we can find thatx=2.666.... or 8/3y=8.333.... or 25/3Thus, the intersecting point is (8/3, 25/3)Solving for coordinates of intersection between linesResources1) http://zonalandeducation.com/mmts/intersections/intersectionOfTwoLines1/intersectionOfTwoLines1.html[This website teaches you step by step on how to derive the coordinates of intersection between lines. It is quite easy to understand and a suitable resource for students who wants to learn about solving coordinates.]2)[It tells you about uses of geometry and coordinate geometry.]## Geometry in Daily Life

BACK TO CHAPTER 5References:1) Secrets of scoring Distinction by Kelvin Lee, chapter 10.6: Linear and Quadratic GraphsExternal Links: 1) Fonts made by http://web2.0write.com/