Question

Which of the following is the equation of the line that is parallel to 2x + y = 3 and passes through the point (1, 2)?

Answer 1

Answer:

2x−3y=1--------(i)

⇒−3y−1−2x

⇒y=

3

2x

−1

[y=mx+c]

∴m=

3

2

equation of line AB

x−x

1

y−y

1

=

x

2

−x

1

y

2

−y

1

x−1

y−3

=

1−1

−7−3

x−1

y−3

=0

⇒y−3=0

⇒y=3

From (i)

2x−3y=1

2x−3×3=1

⇒2x=10

⇒x=5

p=(x.y)=(5,3)

equation of MN at (5,3)

y−y

1

=m(x−x

1

)

y−3=

3

2

(x−5)

⇒3(y−3)=2(x−5)

⇒3y−9=2x−10

⇒3y−2x=−10+9

⇒3y−2x=−1

2x−3y−1=0

Answer 2

Step-by-step explanation:

Correct option is

A

2x−3y+8=0

Given that,

2x−3y=1--------(i)

⇒−3y−1−2x

⇒y=

3

2x

−1

[y=mx+c]

∴m=

3

2

equation of line AB

x−x

1

y−y

1

=

x

2

−x

1

y

2

−y

1

x−1

y−3

=

1−1

−7−3

x−1

y−3

=0

⇒y−3=0

⇒y=3

From (i)

2x−3y=1

2x−3×3=1

⇒2x=10

⇒x=5

p=(x.y)=(5,3)

equation of MN at (5,3)

y−y

1

=m(x−x

1

)

y−3=

3

2

(x−5)

⇒3(y−3)=2(x−5)

⇒3y−9=2x−10

⇒3y−2x=−10+9

⇒3y−2x=−1

2x−3y−1=0