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Each of the given tables represent a direct proportional relationship. For each table, complete the following.
Question:
PART A: Write an equation for each table that represents the direct proportional relationship.
PART B: For each table, write a sentence to describe the unit rate in context of the information given in the table.

Each of the given tables represent a direct proportional relationship For each table complete the following Question PART A Write an equation for each table tha class=

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akposevictor

Answer/Step-by-step explanation:

Equation representing a direct proportional relationship is given as y = mx

Where, unit rate (m) = y/x

Use the above to solve the problems given

PART A:

1. First, find m using a pair fo values from the table, say (2, 30)

m = 30/2 = 15

Substitute m = 15 into y = mx

Equation would be:

y = 15x

2. Find m using (2, 8)

m = 8/2 = 4

Substitute m = 4 into y = mx

Equation would be:

y = 4x

3. Find m using (3, 69)

m = 69/3 = 23

Substitute m = 23 into y = mx

Equation would be:

y = 23x

PART B:

1. Unit rate is 15 pieces of Candy per box of Candy

2. Unit rate is 4 Lemons used per glass of Lemonade

3. Unit rate is 23 gallons of water used per minute

MrRoyal

Direct relationships are used to represent linear functions that pass through the origin.

  • The direct proportional relationship of the tables are: [tex]y = 15x[/tex], [tex]y = 4x[/tex] and[tex]y = 23x[/tex].
  • The unit rates are 15 pieces in 1 candy box, 4 lemons in 1 glass and 23 gallons in 1 minute

Part (a) The equation that represents the direct proportional relationship

A proportional relationship is represented as:

[tex]y = kx[/tex]

Where the proportionality constant (k) is calculated using:

[tex]k = \frac yx[/tex]

From the tables, we have the following points:

  • Table 1: [tex](x,y) = (10,150)[/tex].
  • Table 2: [tex](x,y) = (6,24)[/tex].
  • Table 3: [tex](x,y) = (6,138)[/tex].

So, the proportionality constants for the tables are:

  • Table 1: [tex]k =\frac{150}{10}=15[/tex]
  • Table 2: [tex]k =\frac{24}{6}=4[/tex].
  • Table 3: [tex]k =\frac{138}{6}=23[/tex].

Substitute values for k in [tex]y = kx[/tex].

So, the direct proportional relationship of the tables are:

  • Table 1: [tex]y = 15x[/tex]
  • Table 2: [tex]y = 4x[/tex]
  • Table 3: [tex]y = 23x[/tex].

Part (b) Describe the unit rates

Table (1) represents the pieces of candy in the box of candies.

So, the unit rate is 15 pieces in 1 candy box

Table (2) represents the lemons used for glasses of lemonade

So, the unit rate is 4 lemons in 1 glass

Table (3) represents the gallons of water used in minutes

So, the unit rate is 23 gallons in 1 minute

Read more about proportional relationships at:

https://brainly.com/question/3202565

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