2*x* - 3*y* = -6

**Let’s first find the x-intercept**.

What value are we going to use for

You are correct if you said

***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**

So **the ordered pair (1, 8/3) is another solution** to our function.

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:**

*x* = 3*y*

**Let’s first find the x-intercept**.

What value are we going to use for

You are correct if you said

**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**

So **the ordered pair (1, 1/3) is another solution** to our function.

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

***Replace x with
-1**

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

So **the ordered pair (-1, -1/3) is another solution** to our function.

**The solutions that we found are:**

*x* = 4

This is in the form *x* = *c.*

So, what type of line are we going to end up with?

Vertical.

So, what type of line are we going to end up with?

Vertical.

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?**

**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:**

*y *+ 5 = 0

If you subtract 5 from both sides, you will have *y* = -5. It looks like it fits the form* y* = *c.*

With that in mind, what kind of line are we going to end up with?

Horizontal.

With that in mind, what kind of line are we going to end up with?

Horizontal.

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:**

Last revised on July 3, 2011 by Kim Seward.

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