Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 15: The Slope of a Line
Answer/Discussion
to 1a
(3, 5) and (1, 8) 

*Plug in x and y values into slope formula
*Simplify

Answer/Discussion
to 1b
(4, 2) and (4, 2) 

*Plug in x and y values into slope formula
*Simplify

Answer/Discussion
to 2a
First, we need to write it in the slope/intercept form: 

*Sub. 2x from
both sides
*Inverse of mult. by 4 is div. by 4
*Written in slope/intercept form

Lining up the form with the equation we got, can you see what the slope
and yintercept are?
It looks like our slope is 1/2 and our yintercept
is 2.
(return to
problem 2a) 
Answer/Discussion
to 2b
x = 2
Note how we do not have a y. This
type of linear equation was shown in Tutorial
14 (Graphing Linear Equations). When we have x = c, where c is
a constant, then this graph is what type of line?
If you said vertical, you are correct.
Since this is a special type of linear equation that can't be written
in the slope/intercept form, I'm going to give you a visual of what is
happening and then from that let's see if we can't figure out the slope
and yintercept.
The graph would look like this:

First, let's talk about the slope. Note that all the x values
on this graph are 2. That means the change in x,
which is the denominator of the slope formula, would be 2  (2) = 0.
Well you know that having a 0 in the denominator is a big no no.
This means the slope is undefined. As shown above, whenever you
have a vertical line your slope is undefined.
Now, let's look at the yintercept.
Looking at the graph, you can see that this graph never crosses the yaxis,
therefore there is no yintercept either.
Another way to look at this is the x value
has to be 0 when looking for the yintercept
and in this problem x is always 2.
Final answer, the slope is undefined and the yintercept
does not exist.
(return to
problem 2b) 
Answer/Discussion
to 2c
y = 1
Note how we do not have an x. This
type of linear equation was shown in Tutorial
14 (Graphing Linear Equations). When we have y = c, where c is a constant, then this graph is what type of line?
If you said horizontal, you are correct.
Since this is a special type of linear equation that can't be written
in the slope/intercept form, I'm going to give you a visual of what is
happening and then from that let's see if we can't figure out the slope
and yintercept.
The graph would look like this:

First, let's talk about the slope. Note how all of the y values on this graph are 1. That means the change in y,
which is the numerator of the slope formula would be 1  (1) = 0. Having
0 in the numerator and a nonzero number in the denominator means only
one thing. The slope equals 0.
Now, let's look at the yintercept.
Looking at the graph, you can see that this graph crosses the yaxis
at (0, 1). So the yintercept is (0, 1).
The slope is 0 and the yintercept is
1.
(return to
problem 2c) 
Answer/Discussion
to 3a
and
Rewriting the first equation in slope/intercept form we get: 
The slope of that first equation is 3 and the slope of the
2nd equation is 1/3.
It appears that these slopes are negative reciprocals of each other,
so that means the lines would have to be perpendicular to each other.
(return to problem
3a) 
Answer/Discussion
to 3b
and
The equations are already in the slope/intercept form, so let's go right
to looking for the slope. What did you find?
I found that the slope of the first equation is 5 and the slope
of the second equation is 1/5. So what does that mean?
Well, since the two slopes are negative reciprocals of each other, the lines have to be perpendicular.
(return to problem
3b) 
Last revised on July 3, 2011 by Kim Seward.
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