My head is hurting because of this math problem...........?

Question

a line passes through a( 3,7), b (-4,9). find the value of a if c(a,1) is on the line.

also please help me on this one:
the product of the slopes of two nonvertical perpendicular lines is always -1. Is it possible for two perpendicular lines to both have positive slope? explain.

thank you!will pick best answer.

Answer 1

First part.
Work out the equation of the line that passes through a and b. Personally I am used to the form y = mx + d (actually I would use c at the end, but that could get confusing here as it's the third point in the question).

So once you have the equation, linking x and y, plug y=1 into it and solve for x. That will give you the coordinates of point c.


Second part:
Two ways of looking at it.
The statement clearly says that, if both lines are non-vertical, the product of their slopes is -1. But you cannot multiply two positives to get a negative, so the answer to that question is no.
Another way of looking at it is to think geometrically - if you pick any line with positive slope, how can the slope of the perpendicular be positive too?

Answer 2

Just intutively for the first part: in going from y=9 to y=7 (a decrease of 2) x goes from -4 to 3 or a total of 7 increase so in going from 7 to 1 you should see an increase of 21 so a should be 3 + 21 or 24. a=24

No since two positive numbers multiplied cannot yeild a negative number. if xy = -1, y=-1/x so y and x must have different signs. Likewise you can't have two negative slopes perpendicular.

Answer 3

From the first two points, find the equation of the line. Once you have the equation you can put 1 as y to find a (that'd be x).
You can use this for help: http://www.cut-the-knot.org/Curriculum/Calculus/StraightLine.shtml