Cartesian Coordinate System - Pre-Calculus
Card 0 of 8
Given 
, which graph is the correct one?
Given
First, solve for 
: 
.
Then, graph the 
at 
.
Since the slope of the line is 
, you can graph the point 
as well.
There is only one graph that fits these requirements.
First, solve for
Then, graph the
Since the slope of the line is
There is only one graph that fits these requirements.
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Which of the following does not lie on the line given by the equation below?
Which of the following does not lie on the line given by the equation below?
To determine if a point lies on a line, plug in the x-value and y-value to see if the equation is satisfied. We can do this for each choice to check.
For example:
: 
Since both sides are equivalent, this point does lie on the line.
We can continue to do this for each of the points until one point does not work out.
Thus, this point does not lie on the line. Thus, this must be the solution.
To determine if a point lies on a line, plug in the x-value and y-value to see if the equation is satisfied. We can do this for each choice to check.
For example:
Since both sides are equivalent, this point does lie on the line.
We can continue to do this for each of the points until one point does not work out.
Thus, this point does not lie on the line. Thus, this must be the solution.
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The point 
is in which quadrant?
The point
In order to determine in which quadrant the point lies, we must remember the order of the quadrants. The first quadrant is that where x and y are both positive, to the upper right of the origin. To move sequentially to the final quadrant, we go counterclockwise from the first quadrant, which means the second is where x is negative and y is positive, the third is where x and y are both negative, and the fourth is where x is positive and y is negative. We can see from our point (-3,-8) that x and y are both negative, which means the point lies in the third quadrant.
In order to determine in which quadrant the point lies, we must remember the order of the quadrants. The first quadrant is that where x and y are both positive, to the upper right of the origin. To move sequentially to the final quadrant, we go counterclockwise from the first quadrant, which means the second is where x is negative and y is positive, the third is where x and y are both negative, and the fourth is where x is positive and y is negative. We can see from our point (-3,-8) that x and y are both negative, which means the point lies in the third quadrant.
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Which of the following coordinates does NOT fit on the graph of the corresponding function?
Which of the following coordinates does NOT fit on the graph of the corresponding function?
When looking at the graph, it is clear that when 
, 
has a value less than 
. If we were to plug in the value of 
, our equation would come out as such:
Therefore, at 
, we get a 
, providing the coordinate 
.
When looking at the graph, it is clear that when
Therefore, at
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Which of the following 
coordinates does NOT correspond with the given function and graph?
Which of the following
When looking at the graph, it is clear that when 
, 
has a value greater than 
. When we plug in both 
and 
values into the function, it is clear that these values do not work for the function:
When looking at the graph, it is clear that when
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Which of the following 
coordinates does NOT correspond with the given function and graph?
Which of the following
If we are to plug 
into our function, the values would not work and both sides of the equation would not be equal:
Therefore, we know that these coordinates do not lie on the graph of the function.
If we are to plug
Therefore, we know that these coordinates do not lie on the graph of the function.
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Which of the following 
coordinates does NOT correspond with the given function and graph?
Which of the following
If we were to plug in the coordinate 
into the function, we will find that it does not equate properly:
Since these values do not equate properly when plugged into the function, we now know that 
does not fit on the provided graph.
If we were to plug in the coordinate
Since these values do not equate properly when plugged into the function, we now know that
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and 
are located on the circle, with 
forming its diameter. What is the area of the circle.
Use the distance formula to find the length of 
.
.
Since the length of 
is that of the diameter, the radius of the circle is 
.
Thus, the area of the circle is
.
Use the distance formula to find the length of
Since the length of
Thus, the area of the circle is
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