Find the equation of the line that passes through points (3,5) and (-6,2). write the equation in slope intercept form.
a. y= 3x+5
b. y= -6x+2
c. y= -6x+5
d. y= 1/3x+4

the common point between lines y= 2x+5 and y= 1/2 x+6 is (3, 1/2).
a. true
b. false

are the following two lines parallel?
y= 5x-7
y= 5x+6
a. yes
b. no

are the following two lines perpendicular?
y= 1/2 x+9
y= 1/2 x+3
a. yes
b. no

1)  gradient of line = Δ y ÷ Δ x
                              = (5 -2) ÷ (3 - (-6))
                              = ¹/₃
   
     using the point-slope form (y-y₁) = m(x-x₁)
     using (3,5)
           (y - 5) = ¹/₃ (x -3)
             y - 5  = ¹/₃x - 1
        ⇒        y =   ¹/₃ x  + 4  [OPTION D]

2)        y =  2x  +  5   (1)
           y = ¹/₂ x  + 6   (2)
       
         by substituting y in (1) for y in (2)

           2x  +  5 = ¹/₂ x  + 6 
                 ³/₂ x = 1
                      x = ²/₃

        by substituting found x (2)

            y = ¹/₂ (²/₃)  + 6
            y = ¹⁹/₃

∴ common point is (²/₃ , ¹⁹/₃)  thus answer is FALSE [OPTION B]

3) Yes [OPTION A]
     This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.

4) No [OPTION B]
       Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other.  Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.

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