What is the slope of any line perpendicular to the line through points 0 5 and -3 -4?

Answer 1

The slope of a line perpendicular to the line through (0,5) and (-3,-4) will have a slope that is "opposite" that of the first line, which will be the negative inverse of the slope of the first line, which is -[1/slope] of the first line. So let's find the slope of that first line and then invert it and change its sign to find the slope of a line perpendicular to it. A line through the points (0,5) and (-3,-4) will have a slope that can be found by a simple formula. We take the change of y divided by the change of x and it's that simple. It's that "rise over run" thing that you may have heard of. Ready? Let's jump. The change of y is the "rise" and the change of x is the "run" in the expression. Using the points given, the rise is from 5 to -4, or -9. (To get from 5 to -4, you have to go 9 units in the - or negative direction.) The run is from 0 to -3 or -3. (To get from 0 to -3, you have to go 3 units in the - or negative direction.) The rise over the run is -9/-3 or 9/3 or 3/1 or 3. Piece of cake. Let's do it the other way around to be sure you've got it, okay? Switch the coordinates from (0,5) and (-3,-4) to (-3,-4) and (0,5) and work it. The rise or change of y is from -4 to 5, which is a rise of 9 in the + or positive direction, or +9. The run or change of x is from -3 to 0, which is a run of 3 in the + or positive direction, or +3. The rise over the run is +9/+3 = 9/3 = 3/1 = 3. The slopes match. And why wouldn't they? Onward. We need to take the negative inverse of that slope to find a line perpendicular to it. Let's do that and be done with our problem. A line perpendicular to another line with the slope 3 will have a slope of - (1/3) or - 1/3 or negative 1/3rd or a negative one third. The slope of a line perpendicular to a line through (0,5) and (-3,-4) is - 1/3 or negative one third.