Answer:
(2, -4) lies in Quadrant IV.
Answer:
(0, 4) lies on the y-axis.
Answer:
This is a FALSE statement, so (0, 5) is a NOT a solution.
This is a TRUE statement, so (4, -4) is a solution.
This is a TRUE statement, so (-4, -6) is a solution.
Answer:
Since we can write it in the standard form Ax + By = C, then we have a linear equation.
This means that we will have a line when we go to graph this.
Solutions:
Answer:
Let's first find the x-intercept.
*Inverse of mult. by 2 is div. by 2
Next we will find the y-intercept.
*Inverse of mult. by -1 is div. by -1
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 -1 is div. by -1
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.
Solutions:
Answer:
Let's first find the x-intercept.
*Inverse of mult. by 4 is div. by 4
Since the x-intercept came out to be (0,
0), then it stands to reason that when we put in 0 for x to find the y-intercept we will get (0,
0).
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:
Let's put in another easy number x = -1:
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.
Solutions:
Answer:
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 - 4. So for our solutions we just need three ordered pairs such that y = - 4.
Note that the y-intercept (where x = 0) is at (0, - 4).
Do we have an x-intercept? The answer is no. Since y has to be - 4, then it can never equal 0, which is the criteria of an x-intercept. Also, think about it, if we have a horizontal line that crosses the y-axis at - 4, it will never ever cross the x-axis.
So some points that we can use are (0, - 4), (1, - 4) and (-1, - 4). These are all ordered pairs that fit the criteria of y having to be 4.
Of course, we could have used other solutions, there are an infinite
number of them.
Solutions:
Answer:
*Simplify
Answer:
*Simplify
Answer:
When I'm working with only the boundary line, I will put an equal sign between the two sides to emphasize that we are working on the boundary line. That doesn't mean that I changed the problem. When we put it all together in the end, I will put the inequality back in.
x-intercept:
*Inverse of mult. by 2 is div. by 2
*x-intercept
y-intercept
*Inverse of mult. by -2 is div. by -2
*y-intercept
Plug in 1 for x to get a third solution:
*Inverse of add 2 is sub. 2
*Inverse of mult. by -2 is div. by -2
Solutions:
Since the original problem has a <, this means it DOES NOT include the boundary line.
So are we going to draw a solid or a dashed line for this problem?
It looks like it will have to be a dashed line.
Putting it all together, we get the following boundary line for this problem:
An easy test point would be (0, 0). Note that it is a point that is not on the boundary line. In fact, it is located above the boundary line.
Let's put (0, 0) into the original problem and see what happens:
Our solution would lie above the boundary line. This means we will shade in the part that is above it.
Note that the gray lines indicate where you would shade your final answer.
Last revised on July 31, 2011 by Kim Seward.
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