Show that the straight lines 3x – 5y + 7 = 0 and 15x + 9y + 4 = 0 are perpendicular.

Given: The straight lines are 3x – 5y + 7 = 0 and

15x + 9y + 4 = 0 .

To Prove: The straight lines are 3x – 5y + 7 = 0 and

15x + 9y + 4 = 0 are perpendicular.

Proof: If two lines are perpendicular, then the product of their slopes is equal to –1.

The slope of the first line,3x –5y + 7 = 0 is

()

The slope of the second line, 15x + 9y + 4 = 0

is ()

⇒

Now the product of these slopes is m1×m2.

⇒

As the product of the slopes is –1, the lines are perpendicular to

each other.