Write The Equation For The Table Below.$\[ \begin{tabular}{|c|c|c|c|c|} \hline Miles (mi) & 50 & 100 & 150 & 200 \\ \hline Cost (\$) & 27.50 & 35.00 & 42.50 & 50.00 \\ \hline \end{tabular} \\]Circle One: Linear Quadratic ExponentialOptions:

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Introduction

In mathematics, a table can be used to represent a relationship between two variables. In this case, we are given a table that shows the cost of traveling a certain distance in miles. The table has four rows, each representing a different distance, and two columns, one for the distance in miles and the other for the cost in dollars. Our goal is to determine the equation that represents the relationship between the distance and the cost.

Analyzing the Table

Let's take a closer look at the table and try to identify any patterns or relationships between the distance and the cost.

Miles (mi) Cost ($)
50 27.50
100 35.00
150 42.50
200 50.00

At first glance, it appears that the cost is increasing as the distance increases. However, the rate of increase is not constant. To determine the type of equation that represents this relationship, we need to examine the data more closely.

Determining the Type of Equation

One way to determine the type of equation is to examine the rate of change between consecutive data points. If the rate of change is constant, then the equation is likely to be linear. If the rate of change is not constant, then the equation may be quadratic or exponential.

Let's examine the rate of change between consecutive data points:

  • Between 50 and 100 miles, the cost increases by $7.50 ($35.00 - $27.50).
  • Between 100 and 150 miles, the cost increases by $7.50 ($42.50 - $35.00).
  • Between 150 and 200 miles, the cost increases by $7.50 ($50.00 - $42.50).

As we can see, the rate of change is constant, which suggests that the equation is likely to be linear.

Writing the Equation

Now that we have determined that the equation is likely to be linear, we can write the equation in the form of y = mx + b, where y is the cost, x is the distance, m is the slope, and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two consecutive data points.

Using the data points (50, 27.50) and (100, 35.00), we can calculate the slope as follows:

m = (35.00 - 27.50) / (100 - 50) = 7.50 / 50 = 0.15

Now that we have the slope, we can write the equation as follows:

y = 0.15x + b

To find the y-intercept, we can use the fact that the equation passes through the point (50, 27.50). Substituting x = 50 and y = 27.50 into the equation, we get:

27.50 = 0.15(50) + b = 7.50 + b

Solving for b, we get:

b = 20.00

Therefore, the equation that represents the relationship between the distance and the cost is:

y = 0.15x + 20.00

Conclusion

In this article, we analyzed a table that showed the cost of traveling a certain distance in miles. We determined that the equation that represents the relationship between the distance and the cost is likely to be linear. We then wrote the equation in the form of y = mx + b, where y is the cost, x is the distance, m is the slope, and b is the y-intercept. The equation is y = 0.15x + 20.00.

References

Discussion

This article demonstrates how to determine the equation that represents a relationship between two variables. The equation is likely to be linear if the rate of change between consecutive data points is constant. The equation can be written in the form of y = mx + b, where y is the cost, x is the distance, m is the slope, and b is the y-intercept.

Keywords

  • Linear equation
  • Quadratic equation
  • Exponential equation
  • Rate of change
  • Slope
  • Y-intercept
  • Cost
  • Distance
  • Relationship between variables
    Frequently Asked Questions: Determining the Equation for a Given Table ====================================================================

Q: What is the first step in determining the equation for a given table?

A: The first step is to analyze the table and try to identify any patterns or relationships between the variables. In this case, we are given a table that shows the cost of traveling a certain distance in miles.

Q: How do I determine if the equation is linear, quadratic, or exponential?

A: To determine the type of equation, you need to examine the rate of change between consecutive data points. If the rate of change is constant, then the equation is likely to be linear. If the rate of change is not constant, then the equation may be quadratic or exponential.

Q: What is the formula for calculating the slope of a linear equation?

A: The formula for calculating the slope of a linear equation is:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two consecutive data points.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept, you can use the fact that the equation passes through the point (x, y). You can substitute x and y into the equation and solve for b.

Q: What is the equation that represents the relationship between the distance and the cost?

A: The equation that represents the relationship between the distance and the cost is:

y = 0.15x + 20.00

Q: Can I use this equation to predict the cost of traveling a certain distance?

A: Yes, you can use this equation to predict the cost of traveling a certain distance. Simply substitute the distance into the equation and solve for the cost.

Q: What are some common mistakes to avoid when determining the equation for a given table?

A: Some common mistakes to avoid include:

  • Not analyzing the table carefully enough to identify patterns or relationships between the variables.
  • Not calculating the slope correctly.
  • Not finding the y-intercept correctly.
  • Not using the correct equation to represent the relationship between the variables.

Q: How can I apply this knowledge to real-world problems?

A: You can apply this knowledge to real-world problems by using the equation to predict costs, prices, or other values based on certain conditions. For example, you could use the equation to predict the cost of traveling a certain distance based on the current fuel prices.

Q: What are some additional resources that I can use to learn more about determining the equation for a given table?

A: Some additional resources that you can use to learn more about determining the equation for a given table include:

  • Online tutorials and videos
  • Math textbooks and workbooks
  • Online forums and discussion groups
  • Professional development courses and workshops

Q: Can I use this knowledge to create my own equations and models?

A: Yes, you can use this knowledge to create your own equations and models. By applying the concepts and techniques learned in this article, you can create your own equations and models to represent real-world relationships and phenomena.

Keywords

  • Linear equation
  • Quadratic equation
  • Exponential equation
  • Rate of change
  • Slope
  • Y-intercept
  • Cost
  • Distance
  • Relationship between variables
  • Equation
  • Model
  • Real-world application