# Algebra 1 : How to find out if a point is on a line with an equation

## Example Questions

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

Which of the following points is not on the line y = 7x + 2?

(0, 2)

(1, 10)

(–2, –12)

(–1, –5)

(2, 16)

(1, 10)

Explanation:

To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation. In the given choices, when we plug in (1, 10) we get 10 = 7 + 2, which is false, making this is the desired answer.

y = 7x + 2

(2, 16) gives 16 = 7(2) + 2 = 14 + 2 = 16

(–1, –5) gives –5 = 7(–1) + 2 = –7 + 2 = –5

(0, 2) gives 2 = 7(0) + 2 = 0 + 2 = 2

(–2, –12) gives –12 = 7(–2) + 2 = –14 + 2 = –12

All of these are true.

(1, 10) gives 10 = 7(1) + 2 = 7 + 2 = 9

10 = 9 is a false statement.

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

Which point is on the line ?

Explanation:

To determine whether a point is on a line, simply plug the points back into the equation. When we plug in (2,7) into the equation of  as  and  respectively, the equation works out, which indicates that the point is located on the line.

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

Which of the following statements is incorrect?

is perpendicular to .

and  both fall on the line .

The points  and  lie on the line .

The lines  and  are parallel.

and  both fall on the line .

Explanation:

Lines that have the same slope are parallel (unless the two lines are identical) and lines with slopes that are opposite-reciprocals are perpendicular. So, the only statements left to evaluate are the two that contain a set of points.

Consider  and .

So the slope, or , is 2.

Plugging the point  into the half-finished equation  gives us a  value of . So that statement is true and the only one that could be the answer is the statement containing  and .

Let's check it just in case.

gives us a slope value of 6, so we can already tell the equation for the line will not be . We have found our answer.

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

Which of these lines go through the point (6,5) on an xy-coordinate plane?

None of the other answers

Explanation:

To find out if a point is on a line, you can plug the points back into an equation. If the values equal one another, then the point must be on a line. In this case, the only equation where (6,5) would correctly fit as an  value is .

### Example Question #5 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points are on the line described by the equation?

Two of these answer choices are correct.

Two of these answer choices are correct.

Explanation:

The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for  and the second value for .

If we do this for , we find that

which is true.

The equation also holds true for , but is false for the other values. So, two of the answer choices are correct.

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

Which of the following ordered pairs lies on the line given by the equation ?

Explanation:

To determine which ordered pair satisfies the equation, it would help to rearrange the equation to slope-intercept form.

Then, plug in each ordered pair and see if it satisfies the equation. We are looking for an value that produces the desired answer.

satisfies the equation. All of the other points do not.

(Note: you could also use the original equation in standard form).

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

The point (3,2) is located on which of these lines?

Explanation:

To determine whether a point is on a line, you can plug it into the equation to see if the equation remains valid/equal with the point.

Plugging the point (3,2) into the equation gives you

which works out. None of the other equations would remain equal after pluggin in (3,2).

### Example Question #8 : How To Find Out If A Point Is On A Line With An Equation

The point (2,7) lies on which of these lines?

None of these answers

Explanation:

To determine whether a point is located in a given line, simply plug in the coordinates of the point into the line. In this case, plugging in the coordinates into the only line where you can plug in the coordinates and have a valid equation is . Plugging in (2,7) would give you an equation of , which works out to .

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

Which of these points fall on the graph of the line

Two of these points fall on the graph of this equation.

All three of these points fall on the graph of this equation.

All three of these points fall on the graph of this equation.

Explanation:

To find out if a point is on a line with an equation, we just need to substitute in the point's  and  values and see if the equation holds true. For example, let's look at the point . Substitution into the equation gives us

or

, which is true.

So, this point does fall on the line. Doing the same with the other two points shows us that yes, all three of them fall on the line expressed by this equation.

### Example Question #10 : How To Find Out If A Point Is On A Line With An Equation

Which point is on the line