Is 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?

Question

  if you graph y = 3x+5,  versus the graph of y = -3x+5 ....

 

is there a relationship between the sign (+/-) of the slope of a line and the angle the line makes with the x axis???? Im sure it is straight forward however, I cannot seem to wrap my head around this question.

Answer 1

Mathematically, the answer is definitely "yes"!

 

A line with positive slope rises from left to right, negative slope falls from left to right.

 

When they intersect the x-axis and you measure the angle of the intercept from left to right, two lines with the same magnitude slope but with opposite signs will make the same magnitude intercept angle, but one will be a positive angle and the other a negative angle.  That's the same as saying one approaches the axis from the top side and the other approaches from the bottom.

 

Answer 2

Parviz gave a correct answer by showing how to graph the equation.

 

A simple answer is to realize that the standard "slope-intercept" form of an equation is

     y = mx + b,

Where m is the slope and b is the y-intercept, where the line crosses the y-axis when x = 0.  Imagine you are at the origin of the x-axis and the line is the hill in front of you to your right.  If m is positive, you are climbing the hill, a positive slope.  If m is negative, you are going down hill, a negative slope!

Answer 3

To graph y= 3x +5

 

  The graph can be done by locating 2 points of a line, and connecting them and extending.

   

     easiest way to find 2 points are intercepts.

 

      y = 3x +5 

 

      x=0, y =5   (0,5)  is vertical intercept

 

       y = 0   X = -5/3   ( -5/3, 0) is X intercept, connect those 2 points and get the graph.( graph is increasing  because of positive slope).

   

      Y =-3x +5   (0 ,5) , ( 5/3 , 0 )  connect the intercept points , and get the graph.( graph is decreasing because of negative slope)

  To graph with a point and slope, for first one from y intercept( 0,5) go 3 points rise(up), and 1 point

  right( run).

  2nd one 3 points down(fall), and 1 point right. 

Answer 4

If you think of it in terms of walking, it goes something like this:

 

If you are walking along the x axis (in the positive direction, otherwise you'd be backing up) and you encounter a upward incline you will be walking up, or on a positive slope.  If you encounter an incline going downward then you are on a negative slope.  If you don't encounter any incline then there is no slope or zero slope.  If you hit a vertical wall then you have an ifninite slope.