is the line through points P(-3,-2) and Q(2,3) perpendicular to the line through points R(10,-1) and S(15,-6)

We want to see if the two given lines are perpendicular or not.

We will see that yes, the lines are perpendicular.

First, let's define a general linear equation, it is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the slope of one is equal to the inverse of the opposite of the slope of the other.

Also, if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope of the line is given as:

So we can get the slopes of the two given lines, for line PQ we have:

For line RS we have:

So you can see that the slope of line RS is equal to the inverse of the opposite of line PQ.

Then yes, the lines are perpendicular.

If you want to learn more, you can read:

link

hope this helps you