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Equations

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y = mx + c | ax + by + c = 0 |

y = mx + c

 The equation of the line joining A(-2,4) to B(2,-1)

1) Find the gradient of the line AB Gradient?

2) General rule for a line graph
 (m = gradient)

3) Substitute in a point eg A(-2,4)
to find C (the y-intercept)

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Summary

eg. Find the equation of the line joining (3,2) to (5,6)
  y = mx + c
1) Find the gradient of the line m = rise/run
m = 6-2/5-3
  m = 4/2
  m = 2
  y = 2x + c
 
2) Substitute in one coordinate to find 'c'
x = 3 & y = 2
2 = 2x3 + c
  2 = 6 + c
  c = -4
 
3) Equation of line is... y = 2x - 4

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ax + by + c = 0

 The equation of the line joining A(-2,4) to B(2,-1)
Using the gradient = gradient method

1) Substitute in (x1,y1) & (x2,y2)

2) Find gradient

3) Cross multiply

4) Expand

5) Rearrange to ax+by+c=0



 

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Summary

eg. Find the equation of the line joining (3,6) to (8,2)
Substitute in values y-y1/x-x1 = y1-y2/x1-x2
y-6/x-3 = 6-2/3-8
  y-6/x-3 = 4/-5
multiply by (x - 3)
y - 6 = 4(x-3)/-5
multiply by - 5
-5(y - 6) = 4(x - 3)
Expand brackets
-5y + 30 = 4x - 12
Rearrange so '= 0'
4x + 5y - 42 = 0

 

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