How to find out if a point is on a line with an equation
Help Questions
Math › How to find out if a point is on a line with an equation
Which of the following points is found on the line ?
Explanation
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for
. If the
-value matches the
-coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Which of the following points exist on the line ?
Explanation
The line is a vertical line. This means that any point with an
-value of
will exist on the line.
The only possible point with an -value of
is
.
True or false:
The lines of the equations
and
intersect at the point .
(Note: You are given that the lines are distinct)
False
True
Explanation
If two distinct lines intersect at the point - that is, if both pass through this point - it follows that
is a solution of the equations of both. Therefore, set
in the equations and determine whether they are true or not.
Examine the second equation:
False; is not on the line of this equation.
Therefore, the lines cannot intersect at .
Which of the following points does not belong on the line ?
Explanation
This question asks which of the given points does not belong on the line . This is another way of asking which of the points does the line not pass through.
This question can be quickly solved for by substituting in the given points. This may also be known as the "plug and chug" method. But first, let's rewrite the equation in a more comfortable format with a positive . This can be achieved by multiplying
to both sides of the equation so the result will be:
Each point (coordinate) represents an and a
value through this format:
Simply by arbitrarily substituting in the or
into the equation
and solving for
or
, you can determine if the point belongs on the line if you are left with the given point.
For example, using a point that does belong on the line:
substituting in the value from
, where
, into the equation
, we can solve for
and given that
in the coordinate
, we know that this coordinate would belong.
If we did not receive the anticipated value from the coordinate, we can automatically deduce that the point does not belong on the line. For example, using
and substituting in the
value,
Because , we can deduce that
does not belong on the line
.
Which of the following points is found on the line ?
Explanation
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for
. If the
-value matches the
-coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Which of the following points is found on the line ?
Explanation
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for
. If the
-value matches the
-coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Which point will exist on the line ?
Explanation
The line is a horizontal line with points all
-values equal to
.
The only possible answer with a -value of
is
.
Which point is on the line ?
Explanation
To determine if a point works, plug it in and see if it makes a true statement.
The correct answer does:
Answers that don't work include :
NOT TRUE.
Which of the following points belongs on the line ?
Explanation
This question asks which of the given points belongs on the line . This is another way of asking which of the points does the line pass through.
This question can be quickly solved for by substituting in the given points. This may also be known as the "plug and chug" method.
Each point (coordinate) represents an and a
value through this format:
Simply by arbitrarily substituting in the or
into the equation
and solving for
or
, you can determine if the point belongs on the line if you are left with the given point.
For example, using the point that does belong on the line:
substituting in the value from
, where
, into the equation
, we can solve for
and given that
in the coordinate
, we know that this coordinate would belong.
If we did not receive the anticipated value from the coordinate, we can automatically deduce that the point does not belong on the line. For example, using
and substituting in the
value,
Because , we can deduce that
does not belong on the line
.
Which of the following points does NOT lie on the graph of
Explanation
To find if a point lies on a graph or not, simply plug the x and y values into your equation and see if it holds true. Plugging our x values into the equation gives us the following:
and
So our points are and
. This makes
the only point that does not lie on our graph.