Question

Find equation of the line perpendicular to the line x – 7 y + 5 = 0 and having x intercept 3.

Answer 1

The equation of line is x−7y+5=0 . Also the x intercept of the line which is perpendicular to the line is 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

−7y=−x+( −5 ) y=( −1 −7 )x+( −5 −7 ) y= 1 7 x+ 5 7

Let the slope of line x−7y+5=0 is m 1 and the slope of the line which is perpendicular to this line is m 2 .

Compare the above expression with equation (1).

m 1 = 1 7 c= 5 7

The condition of the perpendicularity of two non vertical lines is given by,

m 1 ⋅ m 2 =−1 m 2 = −1 m 1 (2)

Substitute the value of m 1 in equation (2).

m 2 = −1 1 7 =−7

Now, the formula for the equation of line having slope m and intercept d is given by,

y=m( x+d ) (3)

Substitute the values of d as 3 and m as −7 in equation (3).

y=−7( x+3 ) y=−7x−21 7x+y+21=0

Thus, the equation of the line perpendicular to the line x−7y+5=0 with x intercept as 3 is 7x+y+21=0 .