How do you find the slope given (c, d) and (c, 1/d)?

Question

Hazel Anglin · Accepted Answer

The slope is undefined and the line is a vertical line through #x# at #c#
Whenever the #x# value of two points of a line are the same value the slope is undefined.

Slope which is the change in #x# versus the change in #y#. Slope is identified by the letter #m# #m = (Deltay)/(Deltax)# #m=(y_2-y_1)/(x_2-x_1)# #(c,d)# and #(c,1/d)# #x_1=c# #y_1=d# #x_2=c# #y_2=1/d# #m = (1/d-d)/(c-c)# #m = (1/d-d/d)/(c-c)# #m = ((1-d)/d)/(0)# Because the numerator is #0# this fraction is undefined #m =# undefined The slope is undefined and the line is a vertical line through #x# at #c# Whenever the #x# value of two points of a line are the same value the slope is undefined.

Julia Adams · Answer

undefined To find the slope given the points $ (c, d) $ and $ (c, \frac{1}{d}) $, you use the formula:

$$ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} $$

Since both points have the same $ x $-coordinate ($ c $), the change in $ x $ is 0. Therefore, the slope is undefined.

Hazel Anglin · Answer

undefined To find the slope given points $(c, d)$ and $(c, \frac{1}{d})$, you can use the formula for slope, which is:

$$ \text{Slope} = \frac{{\text{change in }} y}{{\text{change in }} x}} = \frac{{\text{difference in } y}}{{\text{difference in } x}} $$

Substituting the given points:

$$ \text{Slope} = \frac{{\left(\frac{1}{d} - d\right)}}{{(c - c)}} $$

Simplifying further:

$$ \text{Slope} = \frac{{\frac{1}{d} - d}}{{0}} $$

Since the denominator is zero, the slope is undefined. This means that the given points lie on a vertical line, and there is no slope associated with vertical lines.