Question

Determine if the lines are parallel perpendicular or neither x -y=4 and x+y=9

Answer 1

The line x -y=4 is perpendicular to the line x+y=9.

Explanation:

Here, the equation Line 1 : x - y = 4

and the equation Line 2 : x + y = 9

Now, in the STANDARD FORM OF LINE EQUATION:

y = m x + c, here m = slope of the equation.

Line 1 transforms into : y = x - 4

⇒ Here, slope m 1 = 1

Line 2 transforms into : y = -x + 9

⇒ Here, slope m 2 = -1

Any two given lines in the Cartesian Plane are said to be perpendicular to each other if the product of their slopes is -1

Here, m1 x m2 = (1) x (-1) = (-1)

Hence, the line x -y=4 is perpendicular to the line x+y=9.