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Cartesian Plane, SMB-019

A straight line passes through points `Q(3,-2)` and `R(-1,4)` .

Find the equation of `QR` and express in general form.  (3 marks)

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`2y+3x-5=0`

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`text{Line goes through}\ (3,-2) and (-1,4).`

`text(Using the gradient formula):`

`m` `=(y_2-y_1)/(x_2-x_1)`  
  `=(-2-4)/(3-(-1))`  
  `=-3/2`  

 
`text{Find equation through}\ (3,-2), m=-3/2:`

`y-y_1` `=m(x-x_1)`  
`y-(-2)` `=-3/2(x-3)`  
`2(y+2)` `=-3(x-3)`  
`2y+4` `=-3x+9`  
`2y+3x-5` `=0`  

Cartesian Plane, SMB-018

A straight line passes through points `A(-2,-2)` and `B(1,5)` .

Find the equation of `AB` and express in form  `y=mx+c`.  (3 marks)

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`y=7/3x+8/3`

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`text{Line goes through}\ (-2,-2) and (1,5).`

`text(Using the gradient formula):`

`m` `=(y_2-y_1)/(x_2-x_1)`  
  `=(5-(-2))/(1-(-2))`  
  `=7/3`  

 
`text{Find equation through}\ (1,5), m=7/3:`

`y-y_1` `=m(x-x_1)`  
`y-5` `=7/3(x-1)`  
`y-5` `=7/3x-7/3`  
`y` `=7/3x+8/3`  

Cartesian Plane, SMB-017

Albert drew a straight line through points `P` and `Q` as shown on the graph below.

Find the equation of Albert's line and express in general form.  (3 marks)

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`3y-5x+2=0`

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`text{Line goes through}\ (-2,-4) and (1,1).`

`text(Using the gradient formula):`

`m` `=(y_2-y_1)/(x_2-x_1)`  
  `=(1-(-4))/(1-(-2))`  
  `=5/3`  

 
`text{Find equation through}\ (1,1), m=5/3:`

`y-y_1` `=m(x-x_1)`  
`y-1` `=5/3(x-1)`  
`3y-3` `=5x-5`  
`3y-5x+2` `=0`  

Cartesian Plane, SMB-012

What is the equation of the line `l`?  (2 marks)
 

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`y = -2x + 2`

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`l\ text{passes through (0, 2) and (1, 0)}`

`text(Gradient)` `= (y_2-y_1)/(x_2-x_1)`
  `= (0-2)/(1-0)`
  `= -2`

 
`y\ text(intercept = 2)`

`:.y = -2x + 2`

Linear Functions, 2UA 2008 HSC 2b

Let  `M`  be the midpoint of  `(-1, 4)`  and  `(5, 8)`.

Find the equation of the line through  `M`  with gradient  `-1/2`.   (2 marks)

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`x + 2y-14 = 0`

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`(-1,4)\ \ \ (5,8)`

`M` `= ( (x_1 + x_2)/2, (y_1 + y_2)/2)`
  `= ( (-1 + 5)/2, (4 + 8)/2)`
  `= (2, 6)`

 

`text(Equation through)\ (2,6)\ text(with)\ m = -1/2`

`y-y_1` `= m (x-x_1)`
`y-6` `= -1/2 (x-2)`
`2y-12` `= -x + 2`
`x + 2y-14` `= 0`