Question

show that the straight lines 2x+3y-9=0 and 3x-2y+10=0 are at right angles

Answer 1

Consider 2x+3y-9, write it in the form y = mx + c, so
$y = - 2x \div 3 + 9 \div 3$
So m = -2/3

Now consider 3x - 2y + 10 = 0
$y = 3x \div 2 + 10 \div 2$
So m = 3/2

Now we know, eq. of two perpendicular lines is -1
(3/2) * (-2/3) = -1 [Hence proved]