How to find out if a point is on a line with an equation - GRE Quantitative Reasoning
Card 1 of 80
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Tap to reveal answer
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
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Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Tap to reveal answer
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
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Find the point where the line y = .25(x – 20) + 12 crosses the x-axis.
Find the point where the line y = .25(x – 20) + 12 crosses the x-axis.
Tap to reveal answer
When the line crosses the x-axis, the y-coordinate is 0. Substitute 0 into the equation for y and solve for x.
.25(x – 20) + 12 = 0
.25_x_ – 5 = –12
.25_x_ = –7
x = –28
The answer is the point (–28,0).
When the line crosses the x-axis, the y-coordinate is 0. Substitute 0 into the equation for y and solve for x.
.25(x – 20) + 12 = 0
.25_x_ – 5 = –12
.25_x_ = –7
x = –28
The answer is the point (–28,0).
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Determine the greater quantity:
or
Determine the greater quantity:
or
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is the length of the line, except that 
is double counted. By subtracting , we get the length of the line, or 
.
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Which of the following sets of coordinates are on the line 
?
Which of the following sets of coordinates are on the line
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when plugged in for 
and 
make the linear equation true, therefore those coordinates fall on that line.
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
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Which of the following points can be found on the line 
?
Which of the following points can be found on the line
Tap to reveal answer
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point 
lies on this line. None of the other given answer options will result in a true equality.
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point
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On a coordinate plane, two lines are represented by the equations 
and 
. These two lines intersect at point 
. What are the coordinates of point 
?
On a coordinate plane, two lines are represented by the equations
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You can solve for the 
within these two equations by eliminating the 
. By doing this, you get 
.
Solve for 
to get 
and plug 
back into either equation to get the value of 
as 1.
You can solve for the
Solve for
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If the two lines represented by 
and 
intersect at point 
, what are the coordinates of point 
?
If the two lines represented by
Tap to reveal answer
Solve for 
by setting the two equations equal to one another:
Plugging 
back into either equation gives 
.
These are the coordinates for the intersection of the two lines.
Solve for
Plugging
These are the coordinates for the intersection of the two lines.
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Which of the following set of points is on the line formed by the equation 
?
Which of the following set of points is on the line formed by the equation
Tap to reveal answer
The easy way to solve this question is to take each set of points and put it into the equation. When we do this, we find the only time the equation balances is when we use the points 
.
For practice, try graphing the line to see which of the points fall on it.
The easy way to solve this question is to take each set of points and put it into the equation. When we do this, we find the only time the equation balances is when we use the points
For practice, try graphing the line to see which of the points fall on it.
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Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Tap to reveal answer
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
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Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Tap to reveal answer
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
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Find the point where the line y = .25(x – 20) + 12 crosses the x-axis.
Find the point where the line y = .25(x – 20) + 12 crosses the x-axis.
Tap to reveal answer
When the line crosses the x-axis, the y-coordinate is 0. Substitute 0 into the equation for y and solve for x.
.25(x – 20) + 12 = 0
.25_x_ – 5 = –12
.25_x_ = –7
x = –28
The answer is the point (–28,0).
When the line crosses the x-axis, the y-coordinate is 0. Substitute 0 into the equation for y and solve for x.
.25(x – 20) + 12 = 0
.25_x_ – 5 = –12
.25_x_ = –7
x = –28
The answer is the point (–28,0).
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Determine the greater quantity:
or
Determine the greater quantity:
or
Tap to reveal answer
is the length of the line, except that is double counted. By subtracting , we get the length of the line, or .
← Didn't Know|Knew It →
Which of the following sets of coordinates are on the line ?
Which of the following sets of coordinates are on the line
Tap to reveal answer
when plugged in for and make the linear equation true, therefore those coordinates fall on that line.
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
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Which of the following points can be found on the line ?
Which of the following points can be found on the line
Tap to reveal answer
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point lies on this line. None of the other given answer options will result in a true equality.
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point
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On a coordinate plane, two lines are represented by the equations and . These two lines intersect at point . What are the coordinates of point ?
On a coordinate plane, two lines are represented by the equations
Tap to reveal answer
You can solve for the within these two equations by eliminating the . By doing this, you get .
Solve for to get and plug back into either equation to get the value of as 1.
You can solve for the
Solve for
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If the two lines represented by and intersect at point , what are the coordinates of point ?
If the two lines represented by
Tap to reveal answer
Solve for by setting the two equations equal to one another:
Plugging back into either equation gives .
These are the coordinates for the intersection of the two lines.
Solve for
Plugging
These are the coordinates for the intersection of the two lines.
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Which of the following set of points is on the line formed by the equation ?
Which of the following set of points is on the line formed by the equation
Tap to reveal answer
The easy way to solve this question is to take each set of points and put it into the equation. When we do this, we find the only time the equation balances is when we use the points .
For practice, try graphing the line to see which of the points fall on it.
The easy way to solve this question is to take each set of points and put it into the equation. When we do this, we find the only time the equation balances is when we use the points
For practice, try graphing the line to see which of the points fall on it.
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Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Tap to reveal answer
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
← Didn't Know|Knew It →
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Tap to reveal answer
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
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