CPhill

 y= -3/2x - 3

Slope  =  -3/2

y intercept  =   -3

-3x + 4y= -8       we want to get y by itself  

add 3x to  both sides

4y  =  3x - 8      divide both sides by  4

y  =  (3/4)x - 2      this is the slope-intercept form

The slope is  (3/4)    and the y intercept is  -2 

Slope  =  (-1/2)

Y intercept  =  3   = ( 0, 3) =  1st point

From  (0,3)   we use the slope.......go down 1 in y  and over 2 on x

So.......the 2nd point is  ( 2 , 2)       

Connect the two points with a line.......there's your  graph  !!!!

5)  Since BAD  is trisected,  angle SAD = 30°

And triangle SAD  is a 30 - 60 - 90  triangle

So.......AD  =  √3SD  = √3 * 1  = √3

And angle TAD  = 60°    so   triangle  ATD  is also a 30 - 60 - 90  triangle

And TD  =  √3 AD  =  √3 √3  =  3

So CD  = CT + TD  = 2√3 - 3  + 3  =  2√3

So......the area of  ABCD  =  CD * AD =  2√3 * √3    =  6  units^2

4)  Since QX bisects  PQR, then  angles  PQX = RQX = QPX  = 30°

Then angle QXP  =  120°...so angle QXR  = 60°

And triangles  QRP and QRX   are   30 - 60 - 90  triangles

So.........since QR is opposite a 30° angle, it is  (1/2)PQ =  (1/2) 4√3  = 2√3

So.......QX =  [ 2 / √3 ] * [ 2√3 ]  =  4

3)  AO  = BO   and CO = DO

Then the angles opposite these sides  =  45°

And since triangles ABO and DCO   are 45 - 45 - 90  triangles

Then    DO  =  DC/√2     and  BO  = AB / √2

So   DO  + BO  =    DC/√2 +  AB/√2   =   [ DC + AB ] / √2

And  DO + BO  = BD  =    [ DC + AB ] / √2   =  [ 5 √2 ]  /  √2  =     5

2)  Draw DB

Then DB   is a hypotenuse of triangles DBA, DBC

And its length  is  √  [  (√13)^2  + (√5)^2 ]  =  √18  = 3√2

Then because BC  = CD  then angle CDB  =   angle CBD  = 45°

So because  triangle  DBC  is a 45 - 45 - 90 triangle, BC  =   [ 3√2  ] / √2  =  3

1)  Draw altitude  BD.....this will bisect angle ABC

Then angle BCA  = 30°

And since  triangle BDC is a 30 - 60- 90 triangle...then  CD  =  [√3 / 2] [ 6 √3]  = 9

And CD  =  (1/2) AC

So   AC  = 2CD =  18

Linear :    implies a variable - usually x  -  raised to the first power

So   y  = x + 3  is a linear graph   [ graph of a straight line ]

Non- linear......  x  raised to some other power

So     y = x^2   is a non-linear  [ curved graph ]

See the difference, here :

https://www.desmos.com/calculator/tikumzyzci

Using synthetic division, we have

-1  [  2    0     0        k           1     ]                              

             - 2    2    -  2      - k + 2                                 

        ____________________                      

        2    -2     2    k - 2   - k + 3 

1  [  3    0      k         0        2        ]

             3      3       k + 3   k + 3

      _____________________

       3     3   k + 3    k + 3    k + 5   

Equate remainders

- k  + 3   =  k +  5

-2k  =  2

-1  =   k