# DETERMINING WHETHER A POINT IS ON A LINE

## About "Determining Whether a Point is on a Line"

Determining Whether a Point is on a Line :

In this section, we are going to learn, how to determine whether a point is on a line.

## Determining Whether a Point is on a Line - Examples

Example 1 :

Decide whether the point (3, -2) is on the line whose equation is

y  =  2x - 8

Solution :

The given point is

(x, y)  =  (3, -2)

Substitute 3 for x and -2 for y in the given equation.

-2  =  2(3) - 8   ?

-2  =  6 - 8   ?

-2  =  -2   (True)

The statement is true, so the point is (3, -2) is on the line.

Example 2 :

Decide whether the point (-2, 8) is on the line whose equation is

y  =  6x + 4

Solution :

The given point is

(x, y)  =  (-2, 8)

Substitute -2 for x and 8 for y in the given equation.

8  =  6(-2) + 4   ?

8  =  -12 + 4   ?

8  =  -8   (False)

The statement is false, so the point (-2, 8) is not on the line.

Example 3 :

Decide whether the point (1, -12) is on the line whose equation is

y  =  -10x - 2

Solution :

The given point is

(x, y)  =  (1, -12)

Substitute 1 for x and -12 for y in the given equation.

-12  =  -10(1) - 2   ?

-12  =  -10 - 2   ?

-12  =  -12   (True)

The statement is true, so the point (1, -12) is on the line.

Example 4 :

Decide whether the point (2, 2) is on the line whose equation is

2x + 3y - 10  =  0

Solution :

The given point is

(x, y)  =  (2, 2)

Substitute 2 for x and 2 for y in the given equation.

2(2) + 3(2) - 10  =  0   ?

4 + 6 - 10  =  0   ?

0  =  0   (True)

The statement is true, so the point (2, 2) is on the line.

Example 5 :

If the point (-1, -5) is on the line 9x - y + k  =  0, find the value of k.

Solution :

The given point is

(x, y)  =  (-1, -5)

Substitute -1 for x and -5 for y in the given equation.

9(-1) - (-5) + k  =  0

-9 + 5 + k  =  0

-4 + k  =  0

k  =  4

So, the value of k is 4.

After having gone through the stuff given above, we hope that the students would have understood, "Determining Whether a Point is on a Line".

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