Math Problems (Negative reciprocal of a vertical line, ...)?

Question

1) Does the negative reciprocal (perpendicular) of a vertical line = a horizontal line?

2) I'm supposed to find the point of intersection of two lines with these equations:
y= x^3 - 4x (verbally: x cubed minus four x) and
y= - (x+2) (aka y= - x - 2 )

I understand that we're supposed to set the equations equal to each other and solve for x, but I still can't figure it out. I end up with x^3 - 3x - 2 = 0 and I don't know where to go from there. I try factoring out an x but that doesn't get me anywhere...


3) This problem I can't figure out. It goes something like this:
"Show that the line with intercepts (a,0) and (0,b) has the following equation:
"x/a + y/b = 1" where "a" and "b" do not equal 0.
(verbally: x over a plus y over b equal one)

I tried putting the points in the point slope form: y-b = -b/a(x-0) and end up with x/a + -ay / bx = 1. Close but not dice...


Any and all help is appreciated! Thank you

Answer 1

2) Check it again please :-) The correct equation is: x^3 - 3x + 2 = 0. By a single glance without any calculation we can see that x=1 is a solution of this equation. The point of intersection is (1,-3).

Answer 2

1) No, because the slope of a vertical line does not exist

2) Try completing the square.

3) You're on the right track.

Find the slope of the line:
[y2-y1] / [x2-x1] = [b-0]/[0-a]= -b/a

Now you have a slope and two points to choose from, so put it in point slope form [I used the first point, (a,0)]:
y-y1=m(x-x1)
y-0= -b/a(x-a)
y=(-b/a)x+b
Factor out b:
y= b(-x/a+1)
Divide both sides by b:
y/b = -x/a+1
x/a+y/b =1

Answer 3

Label your points and substitute them into the slope formula. That's all there is to it!