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

## Example Questions

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### Example Question #21 : Other Lines

Which of the following points is on the line ?

Explanation:

Start by rewriting the equation into slope-intercept form.

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.

### Example Question #22 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points is on the line ?

Explanation:

Start by rewriting the equation into slope-intercept form.

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.

### Example Question #23 : 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:

Start by rewriting the equation into slope-intercept form.

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.

### Example Question #24 : How To Find Out If A Point Is On A Line With An Equation

True or false:

The line of the equation passes through the point with coordinates .

True

False

False

Explanation:

A line of an equation passes through the point with coordinates if and only if, when , the equation is true. Substitute for and :

- this is false.

The line does not pass through the point.

### Example Question #25 : How To Find Out If A Point Is On A Line With An Equation

True or false:

The line of the equation passes through the origin.

False

True

True

Explanation:

The coordinates of the origin are , so the line of an equation passes through this point of and only if is a solution of the equation - or, equivalently, if and only if setting and makes the equation a true statement. Substitute both values:

The statement is true, so the line does pass through the origin.

### Example Question #26 : How To Find Out If A Point Is On A Line With An Equation

True or false:

The lines of the equations

and

intersect at the point .

(Note: You are given that the lines are distinct)

True

False

False

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 .

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