Question

Determine whether each equation below does or does not represent a proportional relationship. support your answer using either a table or a graph
equation A: y = x
equation B: y = x+2​

Answer 1

Answer:

• As the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship.
• As the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship.

Step-by-step explanation:

                                        Solving equation A: y = x

Let us consider the given equation A:

                                                      y = x

• Putting x = 1 in y = x

y = x

y = 1    ∵ x = 1

Hence, (1, 1) is the ordered pair of  y = x

• Putting x = 2 in y = x

y = x

y = 2    ∵ x = 2

Hence, (2, 2) is the ordered pair of  y = x

• Putting x = 3 in y = x

y = x

y = 3    ∵ x = 3

Hence, (3, 3) is the ordered pair of  y = x

• Putting x = 4 in y = x

y = x

y = 4    ∵ x = 4

Hence, (4, 4) is the ordered pair of  y = x

• Putting x = 5 in y = x

y = x

y = 5    ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y                 x

1                  1

2                 2

3                 3

4                 4

5                 5

As from the table, lets take the ratio of every point i.e. y/x

• For (1, 1), the ratio will be y/x ⇒ 1/1 = 1
• For (2, 2), the ratio will be y/x ⇒ 2/2 = 1
• For (3, 3), the ratio will be y/x ⇒ 3/3 = 1
• For (4, 4), the ratio will be y/x ⇒ 4/4 = 1
• For (5, 5), the ratio will be y/x ⇒ 5/5 = 1

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

                                          Solving equation A: y = x +2

Let us consider the given equation A:

                                                         y = x + 2    

• Putting x = 1 in y = x + 2

y = x + 2

y = 1 + 2 ⇒ 3  ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

• Putting x = 2 in y = x + 2

y = x + 2

y = 2 +2 ⇒ 4   ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

• Putting x = 3 in y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5    ∵ x = 3

Hence, (3, 5) is the ordered pair of  y = x + 2

• Putting x = 4 in y = x + 2  

y = x + 2  

y = 4 + 2 ⇒ 6   ∵ x = 4

Hence, (4, 6) is the ordered pair of  y = x + 2

• Putting x = 5 in y = x + 2

y = x + 2

y = 5 +2 ⇒ 7    ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y                 x + 2

1                  3

2                 4

3                 5

4                 6

5                 7

As from the table, lets take the ratio of every point i.e. y/x

• For (1, 3), the ratio will be y/x ⇒ 3/1 = 3
• For (2, 4), the ratio will be y/x ⇒ 4/2 = 2
• For (3, 5), the ratio will be y/x ⇒ 5/3 = 5/3
• For (4, 6), the ratio will be y/x ⇒ 6/4 = 3/2
• For (5, 7), the ratio will be y/x ⇒ 7/5 = 7/5

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

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