Coordinate Geometry - SSAT Upper Level Quantitative (Math)
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For the line
Which one of these coordinates can be found on the line?
For the line
Which one of these coordinates can be found on the line?
To test the coordinates, plug the x-coordinate into the line equation and solve for y.
y = 1/3x -7
Test (3,-6)
y = 1/3(3) – 7 = 1 – 7 = -6 YES!
Test (3,7)
y = 1/3(3) – 7 = 1 – 7 = -6 NO
Test (6,-12)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (6,5)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (9,5)
y = 1/3(9) – 7 = 3 – 7 = -4 NO
To test the coordinates, plug the x-coordinate into the line equation and solve for y.
y = 1/3x -7
Test (3,-6)
y = 1/3(3) – 7 = 1 – 7 = -6 YES!
Test (3,7)
y = 1/3(3) – 7 = 1 – 7 = -6 NO
Test (6,-12)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (6,5)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (9,5)
y = 1/3(9) – 7 = 3 – 7 = -4 NO
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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.
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
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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Which of the following sets of coordinates are on the line 
?
Which of the following sets of coordinates are on the line
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
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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Which of the following points is on both the line
and the line
Which of the following points is on both the line
and the line
In the multiple choice format, you can just plug in these points to see which satisfies both equations. 
and 
work for the first but not the second, and 
and 
work for the second but not the first. Only 
works for both.
Alternatively (or if you were in a non-multiple choice scenario), you could set the equations equal to each other and solve for one of the variables. So, for instance,
and 
so 
Now you can solve and get 
. Plug this back into either of the original equations and get 
.
In the multiple choice format, you can just plug in these points to see which satisfies both equations.
Alternatively (or if you were in a non-multiple choice scenario), you could set the equations equal to each other and solve for one of the variables. So, for instance,
and
so
Now you can solve and get
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A line has the equation 
. Which of the following points lies on the line?
A line has the equation
Plug the x-coordinate of an answer choice into the equation to see if the y-coordinate matches with what comes out of the equation.
For 
,
Plug the x-coordinate of an answer choice into the equation to see if the y-coordinate matches with what comes out of the equation.
For
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Which of the following points lies on the line with equation 
?
Which of the following points lies on the line with equation
To find which point lies on the line, plug in the x-coordinate value of an answer choice into the equation. If the y-coordinate value that comes out of the equation matches that of the answer choice, then the point is on the line.
For 
,
So then, 
lies on the line.
To find which point lies on the line, plug in the x-coordinate value of an answer choice into the equation. If the y-coordinate value that comes out of the equation matches that of the answer choice, then the point is on the line.
For
So then,
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Which of the following points is on the line with the equation 
?
Which of the following points is on the line with the equation
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For 
,
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For
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Which of the following points lies on the line with the equation 
?
Which of the following points lies on the line with the equation
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For 
,
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For
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Which of the following points lies on the line with the equation 
?
Which of the following points lies on the line with the equation
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For 
,
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For
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Which of the following points lies on the line with the equation 
?
Which of the following points lies on the line with the equation
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For 
,
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For
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Which of the following points lies on the line with the equation 
?
Which of the following points lies on the line with the equation
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For 
,
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For
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Which of the following lines is parallel to:
Which of the following lines is parallel to:
First write the equation in slope intercept form. Add 
to both sides to get 
. Now divide both sides by 
to get 
. The slope of this line is 
, so any line that also has a slope of 
would be parallel to it. The correct answer is 
.
First write the equation in slope intercept form. Add
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Which pair of linear equations represent parallel lines?
Which pair of linear equations represent parallel lines?
Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "
" spot in the linear equation 
,
We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.
Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "
We are looking for an answer choice in which both equations have the same
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Which of the following equations represents a line that is parallel to the line represented by the equation 
?
Which of the following equations represents a line that is parallel to the line represented by the equation
Lines are parallel when their slopes are the same.
First, we need to place the given equation in the slope-intercept form.
Because the given line has the slope of 
, the line parallel to it must also have the same slope.
Lines are parallel when their slopes are the same.
First, we need to place the given equation in the slope-intercept form.
Because the given line has the slope of
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Which of the following lines is parallel to the line 
?
Which of the following lines is parallel to the line
Lines that are parallel have the same slope, so the correct answer must also have the slope of 
.
Lines that are parallel have the same slope, so the correct answer must also have the slope of
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Which of the following lines is parallel to 
?
Which of the following lines is parallel to
Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of 
.
Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of
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Which of the following lines is parallel to the line 
?
Which of the following lines is parallel to the line
First, put the equation in the more familiar 
format to see what the slope of the given line is.
Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of 
.
First, put the equation in the more familiar
Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of
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Which of the following lines is parallel with the line 
?
Which of the following lines is parallel with the line
First, put the given equation in the more familiar 
format to find out the slope of the given line.
Lines that are parallel must share the same slope. Thus, the line that is parallel has a slope of 
.
First, put the given equation in the more familiar
Lines that are parallel must share the same slope. Thus, the line that is parallel has a slope of
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