The Equation Y = 3.5 X Y = 3.5x Y = 3.5 X Represents The Relationship Between X X X , The Number Of Pounds Of Fruit, And Y Y Y , The Price.Which Ordered Pairs Represent An Amount Of Fruit And The Corresponding Price In The Given Equation? Choose ALL

Introduction

In the world of mathematics, equations are used to represent relationships between variables. The equation $y = 3.5x$ is a linear equation that represents the relationship between the number of pounds of fruit ($x$) and the corresponding price ($y$). In this article, we will explore the meaning of this equation and determine which ordered pairs represent an amount of fruit and the corresponding price.

Understanding the Equation

The equation $y = 3.5x$ is a linear equation, which means that it represents a straight line when graphed. The equation is in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is 3.5, which means that for every 1 unit increase in $x$, there is a corresponding increase of 3.5 units in $y$. The y-intercept is 0, which means that the line passes through the origin (0, 0).

Ordered Pairs and the Equation

An ordered pair is a pair of numbers that represents a point on a coordinate plane. In the context of the equation $y = 3.5x$, an ordered pair represents an amount of fruit ($x$) and the corresponding price ($y$). To determine which ordered pairs represent an amount of fruit and the corresponding price, we need to substitute the values of $x$ and $y$ into the equation and check if the equation holds true.

Example 1: (2, 7)

Let's consider the ordered pair (2, 7). To determine if this pair represents an amount of fruit and the corresponding price, we need to substitute the values of $x$ and $y$ into the equation.

x = 2
y = 7
equation = 3.5 * x
print(equation)

When we run this code, we get the output 7.0, which means that the equation $y = 3.5x$ holds true for the ordered pair (2, 7). Therefore, this pair represents an amount of fruit (2 pounds) and the corresponding price ($7).

Example 2: (5, 17.5)

Let's consider the ordered pair (5, 17.5). To determine if this pair represents an amount of fruit and the corresponding price, we need to substitute the values of $x$ and $y$ into the equation.

x = 5
y = 17.5
equation = 3.5 * x
print(equation)

When we run this code, we get the output 17.5, which means that the equation $y = 3.5x$ holds true for the ordered pair (5, 17.5). Therefore, this pair represents an amount of fruit (5 pounds) and the corresponding price ($17.5).

Example 3: (10, 35)

Let's consider the ordered pair (10, 35). To determine if this pair represents an amount of fruit and the corresponding price, we need to substitute the values of $x$ and $y$ into the equation.

x = 10
y = 35
equation = 3.5 * x
print(equation)

When we run this code, we get the output 35.0, which means that the equation $y = 3.5x$ holds true for the ordered pair (10, 35). Therefore, this pair represents an amount of fruit (10 pounds) and the corresponding price ($35).

Conclusion

In this article, we explored the equation $y = 3.5x$ and determined which ordered pairs represent an amount of fruit and the corresponding price. We used Python code to substitute the values of $x$ and $y$ into the equation and checked if the equation held true. We found that the ordered pairs (2, 7), (5, 17.5), and (10, 35) represent an amount of fruit and the corresponding price.

Final Answer

The ordered pairs that represent an amount of fruit and the corresponding price in the given equation are:

• (2, 7)
• (5, 17.5)
• (10, 35)

These pairs satisfy the equation $y = 3.5x$ and represent the relationship between the number of pounds of fruit and the corresponding price.

Introduction

In our previous article, we explored the equation $y = 3.5x$ and determined which ordered pairs represent an amount of fruit and the corresponding price. In this article, we will answer some frequently asked questions about the equation and provide additional insights into its meaning and application.

Q&A

Q: What is the slope of the equation $y = 3.5x$?

A: The slope of the equation $y = 3.5x$ is 3.5. This means that for every 1 unit increase in $x$, there is a corresponding increase of 3.5 units in $y$.

Q: What is the y-intercept of the equation $y = 3.5x$?

A: The y-intercept of the equation $y = 3.5x$ is 0. This means that the line passes through the origin (0, 0).

Q: How do I determine if an ordered pair represents an amount of fruit and the corresponding price?

A: To determine if an ordered pair represents an amount of fruit and the corresponding price, you need to substitute the values of $x$ and $y$ into the equation and check if the equation holds true. If the equation holds true, then the ordered pair represents an amount of fruit and the corresponding price.

Q: Can I use the equation $y = 3.5x$ to calculate the price of a specific amount of fruit?

A: Yes, you can use the equation $y = 3.5x$ to calculate the price of a specific amount of fruit. Simply substitute the value of $x$ (the amount of fruit) into the equation and solve for $y$ (the price).

Q: What if I want to calculate the amount of fruit for a specific price?

A: If you want to calculate the amount of fruit for a specific price, you can rearrange the equation $y = 3.5x$ to solve for $x$. This will give you the amount of fruit that corresponds to the specific price.

Q: Can I use the equation $y = 3.5x$ to compare prices of different fruits?

A: Yes, you can use the equation $y = 3.5x$ to compare prices of different fruits. By substituting the values of $x$ and $y$ into the equation, you can determine which fruit is more expensive and which is less expensive.

Q: What if I want to use the equation $y = 3.5x$ to calculate the total cost of multiple fruits?

A: If you want to calculate the total cost of multiple fruits, you can use the equation $y = 3.5x$ to calculate the cost of each fruit individually and then add up the costs to get the total cost.

Example: Calculating the Total Cost of Multiple Fruits

Let's say you want to buy 2 pounds of apples, 3 pounds of bananas, and 4 pounds of oranges. Using the equation $y = 3.5x$, you can calculate the cost of each fruit individually and then add up the costs to get the total cost.

# Calculate the cost of 2 pounds of apples
x_apples = 2
y_apples = 3.5 * x_apples
print(f"The cost of 2 pounds of apples is ${y_apples:.2f}")
x_bananas = 3
y_bananas = 3.5 * x_bananas
print(f"The cost of 3 pounds of bananas is $y_bananas.2f")

x_oranges = 4
y_oranges = 3.5 * x_oranges
print(f"The cost of 4 pounds of oranges is $y_oranges.2f")

total_cost = y_apples + y_bananas + y_oranges
print(f"The total cost is $total_cost.2f")

When you run this code, you will get the output:

The cost of 2 pounds of apples is $7.00
The cost of 3 pounds of bananas is $10.50
The cost of 4 pounds of oranges is $14.00
The total cost is $31.50

This shows that the total cost of 2 pounds of apples, 3 pounds of bananas, and 4 pounds of oranges is $31.50.

Conclusion

In this article, we answered some frequently asked questions about the equation $y = 3.5x$ and provided additional insights into its meaning and application. We also showed how to use the equation to calculate the price of a specific amount of fruit, compare prices of different fruits, and calculate the total cost of multiple fruits.