Question

Write down the equation of the line parallel to the line y = (−2/3) x + 4

which passes through the point (6, 2).​

Answer 1

Answer

Correct option is

A

2x−3y=−5

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=

3

2

x+

3

8

Therefore, the slope of the line is m=

3

2

.

Now since the equation of the line with slope m passing through a point (x

1

,y

1

) is

y−y

1

=m(x−x

1

)

Here the point is (2,3) and slope is m=

3

2

, therefore, the equation of the line is:

y−3=

3

2

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.

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