21.2 Working with the equation of a line


Finding the slope and y -intercept when given the equation of a line


When an equation of a line is written in the form y = mx + c with the y on its own, then: Slope = m = rise


Slope = m = the coeffi cient of x c = y- intercept = constant


___ run


y


Recall the coeffi cient of x is the number in front of x .


y-intercept c y = mx + c


Slope m


Run Rise x


By the end of this section you should be able to:


● fi nd the slope and the y -intercept when given the equation of a line


● show that a point is on a given line


Discuss and discover


The following are the equations of four different lines. 2x − y + 8 = 0 3x − 2y − 9 = 0


3x + 2y − 4 = 0 x − 4y + 12 = 0


Work with a classmate to complete the following tasks. (i) Rearrange each of the equations into the form y=mx + c . (ii) Determine the slope of the line in each case. (iii) Copy and complete the following table:


Equation of the line Slope Coeffi cient of x Coeffi cient of y 2x − y + 8 = 0


3 x + 2y − 4 = 0 3 x − 2y − 9 = 0 x − 4y + 12 = 0


(iv) Do you notice any connection between the slope of the line and the coeffi cients of x and y in each case?


(v) Hence, given the equation of a line ax + by + c= 0 , write a general expression for the slope of the line.


When an equation of a line is written in the form ax + by + c = 0 with all terms on the left-hand side, then:


Slope = − coeffi cient of x


___________ coeffi cient of y = − a


__ b


When an equation of a line is written in the form ax + by + c = 0 , it is also possible to rearrange it into the form y = mx + c , where the slope is then the coeffi cient of x , and c is the y -intercept.


For example, 2 x + y + 6 = 0 can be rewritten as y = − 2x − 6 , giving a slope of − 2 and a y -intercept of − 6.


344


Linking Thinking 2


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