Intermediate Geometry : How to find out if a point is on a line with an equation

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #1 : Other Lines

A line passes through both the origin and the point . Which of the following points are NOT on the line?

Possible Answers:

Correct answer:

Explanation:

Because the line passes through the origin, all of the points on the line will have an ratio of .  Only  does not meet this requirement.

Example Question #2 : Other Lines

Which of the following points does NOT lie on the graph of 

Possible Answers:

Correct answer:

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. 

Example Question #3 : Other Lines

Which of the following points exists on the line ?

Possible Answers:

Correct answer:

Explanation:

Substitute each answer choice into the equation in question, , in order to test if the equation is valid at the given point

Only  will satisfy the equation on both the left and right side.

Example Question #4 : Other Lines

Which of the following points exist on the line ?

Possible Answers:

Correct answer:

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 .

Example Question #5 : Other Lines

Which point will exist on the line ?

Possible Answers:

Correct answer:

Explanation:

The line  is a horizontal line with points all -values equal to .

The only possible answer with a -value of  is .

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Which point is on the line ?

Possible Answers:

Correct answer:

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, is definitely on the line because when you plug it in, it creates a true equation:

plug in the  and  values

multiply

this is true, so that point is on the line

The point that does not work is :

multiply

subtract

Since this is not true, the point is NOT on the line.

Example Question #4 : Other Lines

Which point is NOT on the line ?

Possible Answers:

Correct answer:

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example,  is definitely on the line because when you plug it in, it creates a true equation:

 plug in the  and  values

 multiply

 this is true, so that point is on the line

The point that does not work is :

 multiply

 subtract

Since this is not true, the point is NOT on the line.

Example Question #2 : How To Find Out If A Point Is On A Line With An Equation

Which point is NOT on the line ?

Possible Answers:

Correct answer:

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example,  is definitely on the line because when you plug it in, it creates a true equation:

 plug in the  and  values

 multiply

 this is true, so that point is on the line

The point that does not work is :

 multiply

 subtract

Since this is not true, the point is NOT on the line.

Example Question #9 : Other Lines

Which point is NOT on the line ?

Possible Answers:

Correct answer:

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example,  is definitely on the line because when you plug it in, it creates a true equation:

 plug in the  and  values

 multiply

this is true, so that point is on the line

The point that does not work is :

 multiply

 subtract

Since this is not true, the point is NOT on the line.

Example Question #10 : Other Lines

The equation of a line is given below:

which point below can be found is NOT on the line?

Possible Answers:

Correct answer:

Explanation:

To find the solution to this problem just do a quick check, pluggin in each point's x and y value into the equation.  Remember coordinates are written with the x-value first, then the y-value (x,y).

If you try each point the only one that doesn't work is (8,2) !

In other words, if the x-value is 8 the y-value should be 4!

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