Draw the graph for following
a) x+y=4
b) 4=2x-y
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Explanation:
2x+y=4...(i)
⇒y=4−2x
If x=0,y=4−2(0)=4−0=4
x=1,y=4−2(1)=4−2=2
x=2,y=4−2(2)=4−4=0
x 0 1 2 3
y 4 2 0 −2
(i) A B C −2
2x−y=4...(ii)
⇒y=2x−4
If x=0,y=2(0)−4=0−4=−4
x=1,y=2(1)−4=2−4=−2
x=2,y=2(2)−4=4−4=0
x 0 1 2 3 4
y −4 −2 0 2 4
(ii) E F G H I
triangle formed by the lines with y -axis ΔAEC coordinates of vertices are A(0,4),E(0,−4) and C(2,0)
Area of ΔAEC=
2
1
Base×Altitude
=
2
1
AE×CO
=
2
1
×[4−(−4)]×(2−0)
=
2
1
×8×2=8
∴ Area of ΔAEC= Square units.
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