Unit 21


Topics covered within this unit: 21.1 Equation of a line


21.2 Working with the equation of a line


21.3 Graphing lines when given the equation of the line


21.4 Point of intersection of two lines (simultaneous equations)


The Learning Outcomes covered in this unit are contained in the following sections:


GT.5b GT.5c AF.4c AF.7c


Key words Equation of a line


y -intercept Collinear points


y 4


YOU ARE HERE


y = x + 3


3 2 1


–3 –2 –1 0 –1


1 x


The equation of a line


Something to think about …


You are playing an online war game in which you are navigating a battleship.


Your mission is to lay mines at the points where the enemy's travel lanes intersect.


The enemy's travel lanes are represented by the following equations. Enemy lane 1: x = − 4 + y Enemy lane 2:


5x − y = 8 Enemy lane 3: x − 2y + 2 = 0


At what three points should you lay your mines?


21.1 Equation of a line


By the end of this section you should be able to: ● fi nd the equation of a line in the form y=mx+c ● fi nd the equation of a line in the form y− y1


=m(x− x1 )


A straight line on the coordinate plane can be described by an equation. When we take the coordinates of a point on the line and substitute them into the equation, the left side will be equal to the right side.


The equation of a line expresses the relationship of each


x value to its corresponding y value, for each point that lies on the line.


We can use the equation to fi nd where the line is located on the coordinate plane. You could consider the equation to be the ‘address’ of the line. No two lines will have the same location, or equation.


Section B Advancing mathematical ideas


339


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