Anya Graphed The Line $ (y - 2) = 3(x - 1) $ On The Coordinate Grid.What Is The Slope Of Anya's Line?A. $ -3 $ B. $ -1 $ C. $ 1 $ D. $ 3 $

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Introduction

In coordinate geometry, the slope of a line is a fundamental concept that helps us understand the relationship between the x and y coordinates of points on the line. The slope is a measure of how steep the line is and can be calculated using the coordinates of two points on the line. In this article, we will explore the concept of slope and how to calculate it using the given equation of a line.

What is Slope?

The slope of a line is a measure of how much the line rises (or falls) vertically for every unit of horizontal distance it covers. It is denoted by the letter 'm' and can be calculated using the formula:

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

where (x1, y1) and (x2, y2) are two points on the line.

Calculating Slope from the Equation of a Line

The equation of a line in slope-intercept form is given by:

y = mx + b

where m is the slope and b is the y-intercept. To calculate the slope from the equation of a line, we can rearrange the equation to isolate the slope term.

Rearranging the Equation

Let's take the given equation of the line:

(y - 2) = 3(x - 1)

To isolate the slope term, we can expand the equation:

y - 2 = 3x - 3

Now, we can add 2 to both sides of the equation to get:

y = 3x - 1

Identifying the Slope

Comparing the rearranged equation with the slope-intercept form, we can see that the slope term is:

m = 3

Therefore, the slope of Anya's line is 3.

Conclusion

In conclusion, the slope of a line is a measure of how steep the line is and can be calculated using the coordinates of two points on the line or from the equation of the line. By rearranging the equation of the line, we can identify the slope term and determine the slope of the line. In this article, we calculated the slope of Anya's line using the given equation and found that the slope is 3.

Key Takeaways

  • The slope of a line is a measure of how steep the line is.
  • The slope can be calculated using the coordinates of two points on the line.
  • The slope can be calculated from the equation of the line by rearranging the equation to isolate the slope term.
  • The slope of Anya's line is 3.

Frequently Asked Questions

  • What is the slope of a line?
  • How do I calculate the slope of a line?
  • Can I calculate the slope from the equation of a line?
  • What is the slope of Anya's line?

Answer Key

  • The slope of a line is a measure of how steep the line is.
  • To calculate the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) or rearrange the equation of the line to isolate the slope term.
  • Yes, you can calculate the slope from the equation of a line by rearranging the equation to isolate the slope term.
  • The slope of Anya's line is 3.
    Slope of a Line: Frequently Asked Questions =====================================================

Introduction

In our previous article, we explored the concept of slope in coordinate geometry and how to calculate it using the equation of a line. In this article, we will answer some frequently asked questions about the slope of a line.

Q: What is the slope of a line?

A: The slope of a line is a measure of how steep the line is. It is a ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Q: How do I calculate the slope of a line?

A: There are two ways to calculate the slope of a line:

  1. Using the coordinates of two points: You can use the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.
  2. Rearranging the equation of the line: You can rearrange the equation of the line to isolate the slope term. For example, if the equation is in slope-intercept form (y = mx + b), the slope is the coefficient of x.

Q: Can I calculate the slope from the equation of a line?

A: Yes, you can calculate the slope from the equation of a line by rearranging the equation to isolate the slope term. For example, if the equation is in slope-intercept form (y = mx + b), the slope is the coefficient of x.

Q: What is the slope of a horizontal line?

A: The slope of a horizontal line is 0. This is because a horizontal line has no vertical change (rise) between any two points on the line.

Q: What is the slope of a vertical line?

A: The slope of a vertical line is undefined. This is because a vertical line has no horizontal change (run) between any two points on the line.

Q: Can the slope of a line be negative?

A: Yes, the slope of a line can be negative. This means that the line slopes downward from left to right.

Q: Can the slope of a line be zero?

A: Yes, the slope of a line can be zero. This means that the line is horizontal.

Q: Can the slope of a line be undefined?

A: Yes, the slope of a line can be undefined. This means that the line is vertical.

Q: How do I use the slope of a line in real-world applications?

A: The slope of a line is used in many real-world applications, such as:

  • Calculating the rate of change of a quantity over time
  • Determining the steepness of a roof or a road
  • Calculating the angle of a slope in civil engineering
  • Determining the rate of change of a stock price in finance

Conclusion

In conclusion, the slope of a line is a fundamental concept in coordinate geometry that helps us understand the relationship between the x and y coordinates of points on the line. By answering some frequently asked questions about the slope of a line, we hope to have provided a better understanding of this concept and its applications in real-world scenarios.

Key Takeaways

  • The slope of a line is a measure of how steep the line is.
  • The slope can be calculated using the coordinates of two points on the line.
  • The slope can be calculated from the equation of the line by rearranging the equation to isolate the slope term.
  • The slope of a horizontal line is 0.
  • The slope of a vertical line is undefined.
  • The slope of a line can be negative, zero, or undefined.

Frequently Asked Questions

  • What is the slope of a line?
  • How do I calculate the slope of a line?
  • Can I calculate the slope from the equation of a line?
  • What is the slope of a horizontal line?
  • What is the slope of a vertical line?
  • Can the slope of a line be negative?
  • Can the slope of a line be zero?
  • Can the slope of a line be undefined?
  • How do I use the slope of a line in real-world applications?

Answer Key

  • The slope of a line is a measure of how steep the line is.
  • To calculate the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) or rearrange the equation of the line to isolate the slope term.
  • Yes, you can calculate the slope from the equation of a line by rearranging the equation to isolate the slope term.
  • The slope of a horizontal line is 0.
  • The slope of a vertical line is undefined.
  • Yes, the slope of a line can be negative.
  • Yes, the slope of a line can be zero.
  • Yes, the slope of a line can be undefined.
  • The slope of a line is used in many real-world applications, such as calculating the rate of change of a quantity over time, determining the steepness of a roof or a road, and calculating the angle of a slope in civil engineering.