SOLUTION: Please help me with this. I am no good at this stuff. Find the slope of the line through the following pairs of points. (-5, -3) and (-5, 2)

Question 73700: Please help me with this. I am no good at this stuff.
Find the slope of the line through the following pairs of points.
(-5, -3) and (-5, 2)

Found 3 solutions by checkley75, Earlsdon, bucky:
Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!
slope=(y2-y1)/(x2-x1)
slope=(2+3)/(-5+5)
slope=5/0 mathematically this infinity but here it is a verticle line through the point x=-5.
the line equation is x=-5.

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
To find the slope of a line through two given points, use the slope formula: where: and are the x- and y-coordinates of one of the two points and and are the x- and y-coordinates of the other point. So, let's find the slope:

Well, as you know, this is an undefined quantity and for slopes, a line whose slope is undefined is a vertical line.
The answer is:
The slope is undefined. The line is a vertical line.

Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
But you can get good at this stuff if you just don't let the math numbers overwhelm you.
.
This problem is a good example of that. If you just look at the numbers it's easy to give
up and say you're no good at it. There is an answer to this problem and with a little thought
you can get it.
.
First, make a sketch. Draw a set of coordinate axes ... a vertical y-axis and a horizontal
x-axis. From the origin where these two axes cross, mark at least 5 units to the left on the
x-axis. From right to left these marks represent -1, -2, -3, -4, -5, -6, ....
.
Now mark up and down the y-axis 4 units up and 4 units down from the origin. Finally
locate the two points you are given. One point is found by going to -5 on the x-axis and
then going vertically down 3 units in the y-direction. This is the point (-5, -3).
To locate the other point go to -5 in the x direction and then go vertically up 2 units
in the y direction. Where you end up is the point (-5, 2). Now what do you notice
about these two points? They lie on a vertical line!!! One is directly above the other.
The line joining them doesn't slant and it isn't horizontal. Slanting lines have a slope
and a horizontal line is a special case because its slope is zero. Recall that the definition
of slope is usually expressed as the change in x divided into the change in y, or maybe
as rise over run. But this case the change in x (or the run) is zero. And you can't divide
anything by zero in math ... that's a no-no!. So the slope of this vertical line is not
defined, does not exist, or maybe is infinity. But however you choose to think about it,
it isn't a nice number.
.
Now you know a little something more about slopes. Vertical lines don't have a defined
slope, horizontal lines have a slope of zero, and slant lines have a slope that can be
expressed as a number. Another tool in your math toolbox. (And see how valuable it was to
make a sketch to help you think about the problem.)
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