Question

s there a relationship between the sign (positive or negative) of the slope of a line and the angle the line makes with the x-axis?

For example, if you graph y = 3x+5, versus the graph of y = -3x+5 discuss how the different slopes affect the angles made with the x axis.

Answer 1

Pretty Girl: My reasoning applies to this situation. Even though you omitted the equations y - 3x+5 and y=-3x+5 before, you could answer the question anyway. Mind going back to our previous discussion?

Answer 2

So theres a relationship between the sign.. @mathmale

Answer 3

hello???

Answer 4

Well, yes. I'd like to see a bit more discussion, however. Given that there is a rel., what is that rel.?

Answer 5

"If the slope of the given line is positive, the angle FROM the x-axis TO the given line is (fill in the blank)"

Answer 6

negative I guess
@mathmale

Answer 7

@mathmale, I don't understand!!

Answer 8

PG: Have you drawn the graph of y=3x+5, as I've asked you to do? That graph could tell you a lot.

Answer 9

Please go ahead: draw y=3x+5.

Answer 10

The tangent of the angle will be dy/dx, which is the slope.
tan @ = slope @ = arc tan (slope).

Answer 11

DWC: That's a great insight for those of us who know Calculus, but PG probably hasn't seen Calculus yet.
DC?

Answer 12

I don't know Calculus

Answer 13

I'll draw y=3x+5 for you if need be, but would prefer you draw it yourself. OK?

Answer 14

MM, good point. I guess one could spell it out as m = (y2 - y1)/(x2 - x1) and thus not need calculus. I should have done that.

Answer 15

@prettygirl12341234

Do you think it could be that a line with a positive slope forms an acute angle with the x-axis and that a line with a negative slope forms an obtuse angle with the x-axis?