College Algebra
Answer/Discussion to Practice Problems
Tutorial 26: Equations of Lines
Answer/Discussion
to 1a
Slope = ½ and passes through the origin. 
What are the two things we need to write an equation of a line????
If you said any point on the line and the slope, you are correct.
Do you know what the ordered pair for the origin is? If
you said (0, 0) you are right on!!! That is the point that we will
be using to plug into our equation.
Looks like we have all the information we need. We are ready to
put our equation together.
Point/Slope Form: 

*Point/slope form of the line 
Next, we want to write it in the Slope/Intercept
Form, which basically means we need to solve for y: 

*Dist. the 1/2 through ( )
*Slope/intercept form of the line 
The equation of the line that passes through the origin and has
a slope of 1/2 is
y  0 = 1/2(x  0) OR y = 1/2x. 
Answer/Discussion
to 1b
Passing through (2, 4) and (1, 1). 
What are the two things we need to write an equation of a line????
If you said any point on the line and the slope, you are correct.
We have more than enough points. However, what about the slope?
Does this mean we can't work out the problem? You are not going to
get off that easily. We do have a way of finding the slope. Tutorial
25: The Slope of a Line shows us how we can get the slope given two points.
Let's find that slope: 

*Slope formula
*Plug in values
*Simplify

OK, now we have our slope, which is 5.
Now we want to put the slope and one point into the point/slope equation.
Note that you can use either point to plug in as long as it is a point
that the line passes through. I chose to plug in the point (2, 4).
Point/Slope Form: 

*Point/slope form of the line

Make sure that you are careful when one of your values is negative
and you have to subtract it as we did in line 2. x  (2) is not the same as x  2. 
Next, we want to write it in the Slope/Intercept
Form, which basically means we need to solve for y: 

*Dist. the 5 through ( )
*Inverse of sub. 4 is add 4
*Slope/intercept form of the line 
The equation of the line that passes through the points (2, 4)
and (1, 1) is
y  4 = 5(x + 2) OR y = 5x  6. 
Answer/Discussion
to 1c
xintercept = 5 and yintercept
= 2. 
What are the two things we need to write an equation of a line????
If you said any point on the line and the slope, you are correct.
Do you know what the ordered pair is going to be for the xintercept?
What about the yintercept?
Above, we leaned that an xintercept is where the line crosses the xaxis.
That means y's value is always 0. So
the ordered pair for our xintercept is (5.
0).
Above, we learned that an yintercept is where the line crosses the yaxis.
That means x's value is always 0. So
the ordered pair for our yintercept is (0,
2).
We have more than enough points. However, what about the slope?
Does this mean we can't work out the problem? You are not going to
get off that easily. We do have a way of finding the slope. Tutorial
25: The Slope of a Line shows us how we can get the slope given two points.
Let's find that slope: 

*Slope formula
*Plug in values
*Simplify

OK, now we have our slope, which is 2/5.
We want to put the slope and one point into the point/slope equation.
Note that you can use either point to plug in as long as it is a point
that the line passes through. I chose to plug in the point (5, 0).
Point/Slope Form: 

*Point/slope form of the line

Make sure that you are careful when one of
your values is negative and you have to subtract it as we did in line 2. x  (5) is not the same as x  5. 
Next, we want to write it in the Slope/Intercept
Form, which basically means we need to solve for y: 

*Dist. the 2/5 through ( )
*Slope/intercept form of the line 
The equation of the line that has an xintercept
of 5 and yintercept of 2 is
y  0 = 2/5(x + 5) OR y = 2/5x  2. 
Last revised on Feb. 6, 2010 by Kim Seward.
All contents copyright (C) 2002  2010, WTAMU and Kim Seward. All rights reserved.

