Question

Find equation of the line parallel to the line 3 x – 4 y + 2 = 0 and passing through the point (–2, 3).

Answer 1

The equation of line is 3x−4y+2=0 . The line is passing through the point ( −2,3 ) .

The equation of line having slope m and making an intercept c with the y axis is given by

y=mx+c (1)

Rearrange the terms of the equation

4y=3x+2 y= 3 4 x+ 2 4 y= 3 4 x+ 1 2

Compare the above expression with equation (1).

m= 3 4 ,c= 1 2

The slope of the line is obtained as m= 3 4 .

Any non vertical line whose slope is equal to −3 4 is parallel to the line 3x−4y+2=0 .

Now, the formula for the equation of line passing through the point ( x 1 , y 1 ) and having slope m is given by,

( y− y 1 )=m⋅( x− x 1 ) (2)

Substitute the values of ( x 1 , y 1 ) as ( −2,3 ) and m as −3 4 in equation (2).

( y−3 )= 3 4 ⋅( x−( −2 ) ) 4⋅( y−3 )=3⋅( x+2 ) 4y−12=3x+6 3x−4y+18=0

The equation of the line parallel to the line 3x−4y+2=0 and passing through the point ( −2,3 ) is 3x−4y+18=0 .