The Slope Of The Line Whose Equation Is X − 3 Y = 1 X - 3y = 1 X − 3 Y = 1 Is:A. − 3 -3 − 3 B. − 1 3 -\frac{1}{3} − 3 1 ​ C. 1 3 \frac{1}{3} 3 1 ​

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Introduction

In mathematics, the slope of a line is a fundamental concept that helps us understand the steepness or incline of a line. The slope is a measure of how much the line rises (or falls) vertically over a given horizontal distance. In this article, we will explore the concept of the slope of a line and how to find it using the equation of a line.

What is the Slope of a Line?

The slope of a line is a numerical value that represents the rate of change of the line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope is denoted by the letter 'm' and is usually expressed as a fraction or a decimal.

The Equation of a Line

The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of points on the line. The general form of the equation of a line is:

y = mx + b

where:

  • m is the slope of the line
  • b is the y-intercept (the point where the line intersects the y-axis)
  • x is the independent variable (the input value)
  • y is the dependent variable (the output value)

Finding the Slope of a Line

To find the slope of a line, we can use the equation of the line and rearrange it to isolate the slope (m). Let's consider the equation of the line:

x - 3y = 1

We can rearrange this equation to isolate y:

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

Now, we can see that the slope of the line is 1/3.

The Slope of the Line Whose Equation is x - 3y = 1

The equation of the line is x - 3y = 1. To find the slope of this line, we can rearrange the equation to isolate y:

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

From this equation, we can see that the slope of the line is 1/3.

Conclusion

In conclusion, the slope of a line is a fundamental concept in mathematics that helps us understand the steepness or incline of a line. The slope is a measure of how much the line rises (or falls) vertically over a given horizontal distance. We can find the slope of a line using the equation of the line and rearranging it to isolate the slope. In this article, we have seen how to find the slope of a line whose equation is x - 3y = 1.

The Final Answer

The final answer is:

Q&A: The Slope of a Line

Q: What is the slope of a line?

A: The slope of a line is a numerical value that represents the rate of change of the line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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

A: To find the slope of a line, you can use the equation of the line and rearrange it to isolate the slope (m). The general form of the equation of a line is:

y = mx + b

where:

  • m is the slope of the line
  • b is the y-intercept (the point where the line intersects the y-axis)
  • x is the independent variable (the input value)
  • y is the dependent variable (the output value)

Q: What is the equation of a line?

A: The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of points on the line. The general form of the equation of a line is:

y = mx + b

Q: How do I know if the slope of a line is positive or negative?

A: The slope of a line is positive if the line rises from left to right, and negative if the line falls from left to right.

Q: What is the y-intercept of a line?

A: The y-intercept of a line is the point where the line intersects the y-axis. It is the value of y when x is equal to 0.

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

A: To find the y-intercept of a line, you can set x equal to 0 in the equation of the line and solve for y.

Q: What is the difference between the slope and the y-intercept?

A: The slope of a line represents the rate of change of the line, while the y-intercept represents the point where the line intersects the y-axis.

Q: Can the slope of a line be zero?

A: Yes, the slope of a line can be zero. This occurs when the line is horizontal, meaning that it does not rise or fall.

Q: Can the slope of a line be undefined?

A: Yes, the slope of a line can be undefined. This occurs when the line is vertical, meaning that it does not have a defined rate of change.

Q: How do I graph a line using its equation?

A: To graph a line using its equation, you can use the slope-intercept form of the equation (y = mx + b) and plot the points (0, b) and (1, m + b).

Q: What is the significance of the slope of a line in real-world applications?

A: The slope of a line has many real-world applications, including:

  • Modeling population growth
  • Describing the motion of objects
  • Analyzing financial data
  • Understanding the relationship between variables

Conclusion

In conclusion, the slope of a line is a fundamental concept in mathematics that helps us understand the steepness or incline of a line. The slope is a measure of how much the line rises (or falls) vertically over a given horizontal distance. We can find the slope of a line using the equation of the line and rearranging it to isolate the slope. In this article, we have seen how to find the slope of a line and answered some common questions about the slope of a line.

The Final Answer

The final answer is:

C. 13\frac{1}{3}