Answer/Discussion to 1a

2x - 3y = -6

Let’s first find the x-intercept. 
What value are we going to use for y? 
You are correct if you said y = 0.

*Inverse of mult. by 2 is div. by 2

Next we will find the y- intercept.
What value are we going to plug in for x? 
If you said x = 0, you are right.

*Inverse of mult. by -3 is div. by -3

We can plug in any x value we want as long as we get the right corresponding y value and the function exists there. 

Let’s put in an easy number  x = 1:

*Inverse of add 2 is sub. 2
 

*Inverse of mult. by -3 is div. by -3
 

Note that we could have plugged in any value for x: 5, 10, -25, ...,  but it is best to keep it as simple as possible.
 
 

The solutions that we found are:
 

(return to problem 1a)

Answer/Discussion to 1b

x = 3y

Let’s first find the x-intercept. 
What value are we going to use for y? 
You are correct if you said y = 0.

Next we will find the y- intercept.
What value are we going to plug in for x? 
If you said, x = 0 you are right.

Since we really have found only one point this time, we better find two  additional solutions so we have a total of three points.

We can plug in any x value we want as long as we get the right corresponding y value and the function exists there. 

Let’s put in an easy number  x = 1:

*Inverse of mult. by 3 is div. by 3

Let’s put in another easy number x = -1:

*Replace x with -1

*Inverse of mult. by 3 is div. by 3

The solutions that we found are:
 

(return to problem 1b)

Answer/Discussion to 2a

x = 4

Since this is a special type of line, I thought I would talk about steps 1 and 2 together.

It does not matter what y is, as long as x is 4. 

Note that the x-intercept is at (4, 0).

Do we have a y-intercept?  The answer is no.  Since x can never equal 0, then there will be no y-intercept for this equation.

Some points that would be solutions are (4, 0), (4, 1), and (4, 2).

Again, I could have picked an infinite number of solutions.
 

The solutions that we found are:
 

(return to problem 2a)

Answer/Discussion to 2b

y + 5 = 0

Since this is a special type of line, I thought I would talk about steps 1 and 2 together.

It doesn’t matter what x is, y is always -5.  So for our solutions we just need three ordered pairs such that y = -5. 

Note that the y-intercept (where x = 0) is at (0, -5). 

Do we have a x-intercept? The answer is no.  Since y has to be -5, then it can never equal 0, which is the criteria of an x-intercept. 

So some points that we can use are (0, -5), (1, -5) and (2, -5).  These are all ordered pairs that fit the criteria of y having to be -5.

Of course, we could have used other solutions, there are an infinite number of them.
 

The solutions that we found are:
 

(return to problem 2b)