DETERMINE IF THE POINTS ON A STRAIGHT LINE

How to check if the points lie on the straight line ?

To check if the point (x, y) lie on the line, we have to apply the given point in the equation.

  • If the equation satisfies the given point, then it is the solution.
  • If the equation does not satisfy by the given point, then it is not a solution.

Problem 1 :

Does (3, 4) lie on the line with equation 5x + 2y = 23?

Solution:

5x + 2y = 23

Substitute x = 3 and y = 4 in the equation

5(3) + 2(4) = 23

15 + 8 = 23

23 = 23

Yes, the point lies on the equation.

Problem 2 :

Does (-1, 4) lie on the line with equation 3x - 2y = 11?

Solution:

3x - 2y = 11

Substitute x = -1 and y = 4 in the equation

3(-1) - 2(4) = 11

-3 - 8 = 11

-11 = 11

No, the point does not lies on the equation.

Problem 3 :

Does (5, -1/2) lie on the line with equation 3x + 8y = 11?

Solution:

3x + 8y = 11

Substitute x = 5 and y = -1/2 in the equation

3(5) + 8(-1/2) = 11

15 - 4 = 11

11 = 11

Yes, the point lies on the equation.

Problem 4 :

Find k if:

(2, 5) lies on the line with equation 3x - 2y = k

Solution :

3x - 2y = k

Substitute x = 2 and y = 5 in the equation

3(2) - 2(5) = k

6 - 10 = k

k = -4

Problem 5 :

Find k if:

(-1, 3) lies on the line with equation 5x + 2y = k

Solution:

5x + 2y = k

Substitute x = -1 and y = 3 in the equation

5(-1) + 2(3) = k

-5 + 6 = k

k = 1

Problem 6 :

Find a given that:

(a, 3) lies on the line with equation y = 2x - 11

Solution:

y = 2x - 11

Substitute x = a and y = 3 in the equation

3 = 2a - 11

2a = 11 + 3

2a = 14

a = 14/2

a = 7

Problem 7 :

Find a given that:

(a, -5) lies on the line with equation y = 4 - x

Solution:

y = 4 - x

Substitute x = a and y = -5 in the equation

-5 = 4 - a

-a = -5 - 4

-a = -9

a = 9

Problem 8 :

Find a given that:

(4, a) lies on the line with equation y = 1/2x + 3

Solution:

y = 1/2x + 3

Substitute x = 4 and y = a in the equation

a = 1/2 (4) + 3

a = 2 + 3

a = 5

Problem 9 :

Find a given that:

(-2, a) lies on the line with equation y = 1 - 3x

Solution:

y = 1 - 3x

Substitute x = -2 and y = a in the equation

a = 1 - 3(-2)

a = 1 + 6

a = 7

Problem 10 :

Find b if:

(2, b) lies on the line with equation x + 2y = -4

Solution:

x + 2y = -4

Substitute x = 2 and y = b in the equation

2 + 2b = -4

2b = -4 - 2

2b = -6

b = -6/2

b = -3

Problem 11 :

Find b if:

(-1, b) lies on the line with equation 3x - 4y = 6

Solution:

3x - 4y = 6

Substitute x = -1 and y = b in the equation

3(-1) - 4b = 6

-3 - 4b = 6

-4b = 6 + 3

-4b = 9

b = -9/4

Problem 12 :

Find b if:

(b, 4) lies on the line with equation 5x + 2y = 1

Solution:

5x + 2y = 1

Substitute x = b and y = 4 in the equation

5b + 2(4) = 1

5b + 8 = 1

5b = 1 - 8

5b = -7

b = -7/5

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