Mathematics, 26.01.2021 09:30 anna22684

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

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Answer from: andresduenas72

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

The direct proportional relationship of the tables are: y = 15x

and

.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:

y = kx

Where the proportionality constant (k) is calculated using:

$k = \frac yx$

From the tables, we have the following points:

Table 1:

.Table 2:

.Table 3:

So, the proportionality constants for the tables are:

Table 1: $k =\frac{150}{10}=15$ Table 2: $k =\frac{24}{6}=4$ .Table 3: $k =\frac{138}{6}=23$ .

Substitute values for k in y = kx .

So, the direct proportional relationship of the tables are:

Table 1:

Table 2:

Table 3:

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:

link

Answer from: kimhayleeshook50

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

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$

Answer from: Quest

2/1 or just 2. sorry if i get this wrong

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