SSAT Upper Level Math : How to find out if a point is on a line with an equation
Study concepts, example questions & explanations for SSAT Upper Level Math
All SSAT Upper Level Math Resources
Example Questions
Example Question #43 : Coordinate Geometry
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. 
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 
Example Question #1 : How To Find Out If A Point Is On A Line With An Equation
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 
Example Question #1 : How To Find Out If A Point Is On A Line With An 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, 
Example Question #2 : How To Find Out If A Point Is On A Line With An 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 
Example Question #3 : How To Find Out If A Point Is On A Line With An 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 
Example Question #4 : How To Find Out If A Point Is On A Line With An 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 
Example Question #5 : How To Find Out If A Point Is On A Line With An 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 
Example Question #6 : How To Find Out If A Point Is On A Line With An 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 
Example Question #2 : How To Find Out If A Point Is On A Line With An Equation
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.
44
48
12
21
36
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.
Example Question #3 : Other Lines
For the line
Which one of these coordinates can be found on the line?
(3, –6)
(9, 5)
(6, –12)
(6, 5)
(3, 7)
(3, –6)
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
All SSAT Upper Level Math Resources
