ElectricPavlov

Remember how to find the slope between two points  ?    ( y1-y2) /(x1-x2) = m = slope = 1/3

y = mx + b

y = 1/3 x + b     sub in one of the points to calculate 'b'

-2 = 1/3 (6) + b       then b = -4

y = 1/3 x -4

Need to find side DC via Pythagorean Theorem

8^2 = 4^2 + (DC)^2

DC = sqrt 48

Sin B = opposite side / hypotenuse =   DC /hyp = sqrt 48 / 8       simplify as needed .........

Second method :    Cos B = adjacent side / hypot = 4/8  

  Trig identity:    sin^2 + cos^2 = 1

    then     sin = sqrt (1-cos^2) = sqrt ( 1 - 16/64) = sqrt 48 / 8   

Find two integer points   -3,-1    and     3,3    use them to calculate the slope = 4/6 = 2/3

  b is the y axis intercept    b = 1

y = mx + b     form

y = 2/3 x + 1

-2/3x + y = 1

-2x + 3y = 3             Not sure which you consider 'standard' form.....  You're pick ! 

x^2 + 8x + 16   =     (x+4)^2                  ( take 1/2 of the 'x' coefficient ...then square it....then add it to the equation)

Slope = rise/run =   4/2 = 2

b = y-axis intercept = 3

y = 2x+3

y-2x = 3

-2x+y = 3

19x-8=12x+13       Subtract 12x from both sides of the equation to get

7x-8 = 13               add 8 to both sides to get

7x = 21                    divide both sides by 7

x = 3

Midpoint is   1,6          slope, m, between points is 4/-8 = -1/2    ( you should know how to do this)  

                                      perpindicular slope =  -1/m  =    2   ( you should know this too)

point slope form of your perpindicular line is then:

y-6 = 2 (x-1)    re-arrange

y-6 = 2x - 2

y = 2 x + 4          you can finish .....

Area of   ADE =  1/2 5 x 5 = 25/2

area of  ABC = 1/2  3 * AC  = 25/2

                             AC = 25/3

    AC - AE = EC = 25/3 - 5 = 10/3

p + 2q = 0

q - 2r = 0

p + r = 5            multiply by 2     2p+2r=10    add to second equation to get

q +2p = 10      multiply by -2      -2q-4p= -20   add to top equation

-3p = -20      p = 20/3        then r = - 5/3   (from third equation)      and q = ________    (you can finish !)

slope = (y1-y2)/(x1-x2) = -8/-2 = 4

y = 4x+b    sub in one of the points to find 'b'

0 = 4(-2) +b      b = 8

y = 4x + 8       m + b = 12