Determine the gradient of the straight line 2x-3y+9=0. Find the equation of the straight line through the origin which is perpendicular to the line 2x-3y+9=0.

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x - 3y + 9 = 0 ( subtract 2x + 9 from both sides )

- 3y = - 2x - 9 ( divide terms by - 3 )

y = x + 3 ← in slope- intercept form

with slope m =

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = -

Since the equation passes through the origin then y- intercept is zero , that is c = 0

y = - x ← equation of perpendicular line

step-by-step explanation: