The constant of proportionality is the amount a relationship will change for each unit.

Question

It is represented by the value of this ratio: k=yx

One of the ways a proportional relationship is identified is with an equation.

y=kx

The constant of proportionality (unit rate) is $2.25 per pound. The equation for this relationship is:

y = 2.25x

where y is the cost and x is the pound of oranges.

(8 points)
Determine the equation for each table and graph below.



The constant of proportionality is
and the equation for this relationship is
.

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The constant of proportionality is
and the equation for this relationship is
.

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The constant of proportionality is
and the equation for this relationship is
.

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The constant of proportionality is
and the equation for this relationship is
.



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Answer 1

To determine the constant of proportionality and the corresponding equation from tables or graphs, you will typically look for the ratio of the output to the input values (y/x).

Since no specific tables or graphs were provided in your question, I’ll demonstrate how to derive the constant of proportionality and the equation using sample data.

Example 1

Table:

| x (pounds) | y (cost in $) | |------------|----------------| | 1 | 2.25 | | 2 | 4.50 | | 3 | 6.75 | | 4 | 9.00 |

1. Constant of proportionality (k): Calculate \( k \):

   • For example, for \( x = 1, y = 2.25 \):
   • \( k = \frac{y}{x} = \frac{2.25}{1} = 2.25 \)

2. Equation: Using \( k \), the equation is:

   • \( y = 2.25x \)

So for this table, the entries would be:

• The constant of proportionality is 2.25 and the equation for this relationship is y = 2.25x.

Example 2

Table:

| x (pounds) | y (cost in $) | |------------|----------------| | 1 | 1.50 | | 2 | 3.00 | | 3 | 4.50 | | 4 | 6.00 |

1. Constant of proportionality (k): Calculate \( k \):

   • For \( x = 1, y = 1.50 \):
   • \( k = \frac{y}{x} = \frac{1.50}{1} = 1.50 \)

2. Equation: The equation becomes:

   • \( y = 1.50x \)

So for this table, you would fill in:

• The constant of proportionality is 1.50 and the equation for this relationship is y = 1.50x.

Example 3

Table:

| x (pounds) | y (cost in $) | |------------|----------------| | 1 | 3.00 | | 2 | 6.00 | | 3 | 9.00 | | 4 | 12.00 |

1. Constant of proportionality (k): Calculate \( k \):

   • For \( x = 1, y = 3.00 \):
   • \( k = \frac{y}{x} = \frac{3.00}{1} = 3.00 \)

2. Equation: Thus, the equation is:

   • \( y = 3.00x \)

So for this table:

• The constant of proportionality is 3.00 and the equation for this relationship is y = 3.00x.

Example 4

Table:

| x (pounds) | y (cost in $) | |------------|----------------| | 1 | 4.00 | | 2 | 8.00 | | 3 | 12.00 | | 4 | 16.00 |

1. Constant of proportionality (k): Calculate \( k \):

   • For \( x = 1, y = 4.00 \):
   • \( k = \frac{y}{x} = \frac{4.00}{1} = 4.00 \)

2. Equation: The resulting equation is:

   • \( y = 4.00x \)

So for this table:

• The constant of proportionality is 4.00 and the equation for this relationship is y = 4.00x.

Feel free to provide any specific tables or graphs for a more precise analysis or response!