DETERMINING WHETHER A POINT IS ON A LINE

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

Add 4 to each side. 

k  =  4

So, the value of k is 4.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.