DETERMINE IF THE POINT IS A SOLUTION TO THE EQUATION

Determine whether the given point satisfies the given equation, or in other words the point lies on the graph of the line:

Problem 1 :

(2, 5), y = 4x - 3

Solution :

The given point is

(x, y) = (2, 5)

Substitute 2 for x and 5 for y in the given equation.

5 = 4(2) - 3

5 = 8 - 3

5 = 5

The point (2, 5) satisfies the equation. So, it is a solution and (2, 5) is on the line.

Problem 2 :

(3, -1), y = 2x - 7

Solution :

The given point is

(x, y) = (3, -1)

Substitute 3 for x and -1 for y in the given equation.

-1 = 2(3) - 7

-1 = 6 - 7

-1 = -1

The point (3, -1) satisfies the equation. So, it is a solution and (3, -1) is on the line.

Problem 3 :

(-4, 2), y = -x + 3

Solution :

The given point is

(x, y) = (-4, 2)

Substitute -4 for x and 2 for y in the given equation.

2 = 4 + 3

2 ≠ 7

The point (-4, 2) does not satisfy the equation. So, it is not a solution and (-4, 2) is not on the line.

Problem 4 :

(-1, 7), y = -2x + 5

Solution :

The given point is

(x, y) = (-1, 7)

Substitute -1 for x and 7 for y in the given equation.

7 = -2(-1) + 5

7 = 2 + 5

7 = 7

The point (-1, 7) does not satisfy the equation. So, it is not a solution.

Problem 5 :

(4, -1), y = -2x + 7

Solution :

The given point is

(x, y) = (4, -1)

Substitute 4 for x and -1 for y in the given equation.

-1 = -2(4) + 7

-1 = -8 + 7

-1 = -1

The point (4, -1) satisfies the equation. So, it is a solution.

Problem 6 :

(1, 6), y = -3x + 5

Solution :

The given point is

(x, y) = (1, 6)

Substitute 1 for x and 6 for y in the given equation.

6 = -3(1) + 5

6 = -3 + 5

6 ≠ 2

The point (1, 6) does not satisfy the equation. So, it is not a solution and (1, 6) is not lie on the line.