Algebra: Graphing, Distance between Points and Equations of Line

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P187.

12.)
y = 1/2 x + 1 has no symmetry about either x-axis or y-axis or origin.
(see attached file). --Answer

14.)
y = 2x is unsymmetric about either x-axis or y-axis or origin. --Answer

16.)
|y| = -x
for y> 0 => y = -x
for y < 0 => -y = -x => y = x
=> symmetric about y-axis --Answer

18.)
y = -x => symmetric about origin.

20.)
Distance between points (-6,4) and (2,-1)
s = sqrt ((-6 - 2)^2 + (4 - (-1))^2)
s = sqrt((-8)^2 + (5)^2) = sqrt(64 + 25) = sqrt(89) --Answer

24.)
C =(x1,y1) =(0,0); r = 6
eqn of circle,
(x-x1)^2 + (y-y1)^2 = r^2
=> (x-0)^2 + (y-0)^2 = 6^2
=> x^2 + y^2 = 36 --Answer

28.)
C(-1,-3) = (x1, y1) ; r = sqrt(5)
Eqn of circle,
(x - x1)^2 + (y - y1)^2 = r^2
=> (x - (-1))^2 + (y - (-3))^2 = (sqrt(5))^2
=> (x + 1)^2 + (y + 3)^2 = 5
=> x^2 + 2x + 1 + y^2 + 6y + 9 = 5
=> x^2 + Y^2 + 2x + 6y + 5 = 0 --Answer

32.)
Figure shows the symmetry about y-axis only --Answer(B)

P203.)

22.)
slope (m)= -1, y-intercept (c)= 7
Eqn of straight line:
y = mx + c
=> y = -1*x + 7
=> x + y = 7 ...