I am back studying after a few years away from it and I wonder if someone will be able to give a bit of advice.
The question i am needing help with is this-
Determine the equation of the line perpendicular to 4x+3Y+5=0 passing through the point (2,4).
The notes I have been given for the Maths class are very poor and was wondering if someone could help or maybe send me a link to a good tutorial website.
In order to write the equation for a line we need two pieces of information:
(1) A point on the line
(2) The slope of the line
This problem gives us a point for free: (2,4). Unfortunately we're going to have to work to find the slope. We know that our line is going to be perpendicular to their line (4x+3y+5=0), so if we can find the slope of their line we'll know what ours should be (I'll explain how in a little bit).
Finding the Slope of their line:
To find the slope of a line from its equation just solve for y, and whatever the x coefficient turns out to be, that is the slope...
So the slope of their line is
Find the Slope of our line:
If they had asked us to find a parallel line, we would have our slope already--we'd just use the slope of their line. However, since we're looking for a perpendicular line, we have to make two adjustments to their slope to get ours:
(1) change the sign
(2) take the reciprocal
Changing the sign and taking the reciprocal of gives us .
Writing the equation:
When you've got a point (let's call it ) and a slope (let's call it ), the easiest equation to write is point-slope form:
For us, is (2,4) and is , so just plug the appropriate values in and you'll have your equation!