Algebra 1

1. find gradient 2--6/7-3 = 8/4 = 2

m*m = -1

m= -0.5

sub the information u know into formula

y = mx + c  or   y - y1 = m(x -x1)

y = -0.5x + 0.5

Here is how I would do the second one:

find slope  =  rise/run  = y1-y2 / x1-x2  =  (5- -7)/(2-6) = 12/-4 = -3

Perpindicular slope is    -  1/(-3) = 1/3

Find the midpoint of AB

  x      (2+6)/2 = 4

  y      (5+ -7)/2 = -1      so midpoint is    (4,-1)   and slope is 1/3

            line is     y = 1/3  x  + b     sub in your midpoint to calculate  'b'

                          -1 = 1/3 (4) + b    results in b = -7/3

y = 1/3 x -  7/3

Here is a picture:

#3     A) (8, 1)  B) (0, -1) 

1)  Find the midpoint  =  ( [ 8 + 0] / 2, [ -1 + 1] / 2)  =  (4, 0 )

2) Find the slope  =  [ -1 -1 ] / [ 0 - 8 ] =   -2/ -8 =  1/4

3) Take the negative reciprocal o the slope =  -4

Using the midpoint and  (3)   we have

y = -4(x - 4)

y = -4x + 16

#4       A) (7, 9)   B) (1, 5) 

Midpoint  ( [ 7 + 1] /2 , [ 5 + 9] /2)    =  ( 4, 7)

Slope  =  [9 - 5 ] / [ 7 - 1 ] =  4/6 = 2/3

Neg reciprocal slope = -3/2      (1)

Using  midpoint  and  (1)   we have

y = (-3/2) ( x - 4) + 7

y = (-3/2)x + 6 + 7

y = -(3/2)x + 13