Conjecture
is an educated guess based on known information. Reached by using inductive reasoning
X= 6
Y= 0
Z= -2
CHECK
3x + y -2z =22
3(6) + 0 -2(-2) =22
18 + 0 +4= 22
22=22
x+5y+z =4
6 +5(0)+ -2 =4
6 + 0 +-2 = 4
4=4
x+3z=0
6 + 3(-2) =0
6 -6 = 0
0=0
-4 or
Rise 4 and run 1 to the left (that's what makes it negative)
Remark
All you need is 2 points to get the line of the equation. One is itself (B and B') is the same in both triangles. Now we need to find one more point. Since this is a reflection, the midpoint between C and C' is the second point. That choice of C and C' is completely arbitrary.
Step One
y intercept of the line. That point is B which is (0,1)
Step Two
Find the midpoint between C and C'
C is (-4,-2) and C' is ( 0 , - 4) The midpoint is
C" = (x2 + x1)/2 , (y2 + y1)/2
C" = (-4 + 0 )/2 , (-2 + - 4) / 2
C" = (-4)/2 , - 6/2
C" = (-2, - 3) C" is the midpoint between C and C'
Step 3
Find the equation of the line.
y = ax + b We are trying to find A
y = ax + 1
-3 = a(-2) + 1
-3 - 1 = a(-2)
- 4 = a(-2) Divide by -2
-4/-2 = a
a = 2
The slope of the line is 2
Answer
y = 2x + 1
The answer is to the expression is -18
