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§° î®±±‣®±U®‣¯bµ°ºu®ä š¯æï±°d
†.Hl¬ î®±q®±Ù Hº.Hl¬ N¯‥µ°c±, N®©…±‣®T
x‣®²y®nµ
l¯. ‣¯cýµ°Q‣® þî¯Á¡®N®‣¬
SMRS B.Ed and M.Ed College, Kalaburagi
¯l®²ã‥¬-11
S¯äy¬(w®£µS®¡®±)
„µ²°u®w¯ EuµÛ°ý®S®¡®±
y¯j®u® w®ºq®‣® ïu¯ãtÁ‡®±± œµ²ºv‣®±î® š¯î®±s®ãÁS®¡®±,
ïu¯ãtÁ‡®±± w®£µ‡®±w®±Ý AsµÁ¶š®±î®w®±.
ïu¯ãtÁ‡®±± w®£µ‡®± î®±²© y®․N®©ÞwµS®¡®w®±Ý ïî®․š®±î®w®±
ïu¯ãtÁ‡®±± î®±²©S®¡®w®±Ý w®£µ‡®± î®±²©N® y®․¤š®±î®w®±
ïu¯ãtÁ‡®±± w®£µ‡®±w®±Ý ‣®Yš®±î® N¹ý®©ã œµ²ºu®±î®w®±.
„µ²°u®w¯ºý®S®¡®±
1. w®£µ‡®± î®±²© y®․N®©ÞwµS®¡®±
2. w®£µ‡®±w®±Ý ‣®Yš®±î®¼u®±
„µ²°u®w¯ š®©N®‣®nµS®¡®±
S®oN®‡®±ºq®ä
H‥¬.›.m yµ½ä°bµN®Ô‣¬
yµ½ä°bµN®Ô‣¬ y®‣®uµ
‥µ°š®‣¬ y¯•±ºh‣¬
Hº.Hš¬.y¯î®‣¬ y¯•±ºg¬
›Þ°N®‣¬ î®±q®±Ù îµ±¶N¬
A†Ãyµä°‣®nµ
1. w®£µ Hºu®‣µ°w®±?
2. w®£µS®¡® î®±²©N® Iw®w®±Ý y®ärxvÚ®±î®‣®±?
3. xuµÁ°ý¯ºN®S®¡®± Hºu®‣µ°w®±?
4. w®£µS®¡®ªå N®ºl®±…‣®±î® A£®S®¡®± ‡®¾¯î®î®¼?
5. H‣®l®± A£®S®¡®± ©º…î¯T Zµ°vÚ®±î® †ºu®± ‡®¾¯î®¼u®±?
w®£µS®¡®ªå xuµÁ°ý¯ºN®S®¡®w®±Ý S®±‣®±rš®±î®¼u®‣® …SµÌ A„¯㚮 ¯lµ²°o
x- A£®x’- A£®
y- A£®
y’- A£®
I- X®q®±s®ÁN®II- X®q®±s®ÁN®
IV- X®q®±s®ÁN®III- X®q®±s®ÁN®
0 +1 +2 +3 +4 +5 +6 +7 +8 +9-9 -8 -7 -6 -5 -4 -3 -2 -1 0
7-6-5-4-3-2-1
+1+2+3+4+5+6+7
(+x, +y)(-x, +y)
(+x, -y)(-x, -y)
î®±²© †ºu®±
xuµÁ°ý¯ºN®S®¡®±
Draw following points in the Graph
1) P(-3,5)
0 +1 +2 +3 +4 +5 +6 +7 +8 +9
x- A£®x’- A£®
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
0+1+2+3+4+5+6+7
0-1-2-3-4-5-6-7-8
y- A£®
y’- A£®
P(-3,5)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
1) Q(0,-8)
0 +1 +2 +3 +4 +5 +6 +7 +8 +9
x- A£®x’- A£®
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
0+1+2+3+4+5+6+7
0-1-2-3-4-5-6-7-8
y- A£®
y’- A£®
Q(0,8)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
1) R(4,0)
0 +1 +2 +3 +4 +5 +6 +7 +8 +9
x- A£®x’- A£®
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
0+1+2+3+4+5+6+7
0-1-2-3-4-5-6-7-8
y- A£®
y’- A£®
Q(0,8) R(4,0)
x 1 2 0 -1 -2
y 7 8 6 5 4
Y=x+6
c
v
c
vc
v
c
v
c
v
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® š®ï±°N®‣®oNµÊ S®±‣®±r›
1) S(-4,-9)
-x
-y
S(-4,-9)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
y®¼w®‣¯î®q®Áwµ
D Nµ¡®Tw® †ºu®±S®¡®w®±Ý w®£µ‡®±ªå S®±‣®±r›․
A(4,5)
B(-4,-5)
Y=2x+5
1) A(4,5)
-x
-y
A(4,5)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
1) B(-4,-5)
-x
-y
B(-4,-5)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
x 1 2 0 -1 -2
y 7 9 5 3 -1
Y=2x+5
c
v
c
v
c
vc
vc
v
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® š®ï±°N®‣®oNµÊ S®±‣®±r›
¹©ã¯y®w®
D Nµ¡®Tw® †ºu®±S®¡®w®±Ý w®£µ‡®±ªå S®±‣®±r›․
A(4,-5)
B(-4,5)
Y=3x-10
1) C(4,-5)
-x
-y
C(4,-5)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
1) D(-4,5)
-x
-y
D(-4,5)
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® †ºu®±S®¡®w®±Ý S®±‣®±r›
x 1 2 0 -1 3
y -7 -4 -10 -13 -1
Y=3x-10
c
v
c
v
c
v
c
v
c
v
S¯äy¬w®ªå xuµÁ°ý¯ºN® î®ãµÚ‡®±w®±Ý ›u®ÜSµ²¢› D Nµ¡®Tw® š®ï±°N®‣®oNµÊ S®±‣®±r›
î®±wµNµ©š®
D Nµ¡®Tw® †ºu®±S®¢Sµ w®£µ‡®±ªå †m›‹
P(-3,-5)
Y=(2x-y)
Aºq®b¯Á© Bu¯‹q® š®ºy®w®²â©S®¡®±
https://www.google.co.in/search?q=graph
https://www.khanacademy.org/math

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