Question 1207841
<br>
For the first one, the other tutor uses a basic algebraic method, showing the lines are perpendicular by finding the slopes and showing that the product of the slopes is -1.<br>
A more sophisticated (and faster and easier) method is to use a dot product.<br>
Given two linear equations ax+by=m and cx+dy=n, the dot product is ac+bd -- the product of the x coefficients plus the product of the y coefficients.  The lines are perpendicular only if the dot product is 0.<br>
In the first example, the dot product is (3)(4)+(4)(-3) = 12-12 = 0, so the lines are perpendicular.<br>
With a little experience, you can tell that the lines are perpendicular by inspection.  By comparing the two equations, we see that the coefficients of x and y are switched, with one of them changing sign.  That guarantees that the dot product will be 0 and the lines will be perpendicular.<br>
Here are a couple of quick examples of pair of equations of lines that are perpendicular:
3x-7y=4 and 7x+3y=4
17x+39y=100 and 39x-17y=0<br>