The equation of the straight line passing through the origin and perpendicular to the straight line 2x + 3y – 7 = 0 is

The straight line is passing through the origin and perpendicular to the straight line 2x + 3y – 7 = 0.

Since the straight line is perpendicular to the straight line

2x + 3y – 7 = 0,the product of their slopes will be equal to –1.

Slope of 2x + 3y–7 = 0 is m1.

∴ slope of the perpendicular line will be m2.

Now m1×m2 = –1

⇒

⇒

The equation of the line passing through (x1,y1) and slope as m is:

(y–y1) = m(x–x1)

∴ The equation of the line passing through the origin(0,0) and slope as is:

⇒ 2(y–0) = 3(x–0)

⇒ 2y = 3x–0

⇒ 3x–2y = 0