Slope of Lines

Date: 8/6/96 at 21:34:25
From: Anonymous
Subject: Slope of Lines

i) What is the slope of the line y = -px + 5 if the line goes through 
(0, -3)?

ii) Why does the y-axis have an infinite slope, and the x-axis have a 
slope of 0?

Date: 8/7/96 at 9:19:6
From: Doctor Anthony
Subject: Re: Slope of Lines

(i) The gradient [slope] is the value of -p in your equation.  
Substitute (0, -3) for x and y in the equation, and we get  
-3 = -p(0) + 5   This is clearly not possible unless p is 
infinite.  

The line is in fact the y axis, as can be seen from the fact that it 
goes through (0, 5) and (0, -3), and the y axis has infinite gradient.

(ii) The gradient of a line is the tangent of the angle of slope; that 
is, the tangent of the angle between the line and the positive x axis.

The x axis has angle 0 with itself, so its gradient is tan(0) = 0.

The y axis makes an angle of 90 degrees with the x axis, and tan(90) = 
infinity,  So the y axis has infinite gradient.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/