What Is The Slope Of The Line That Passes Through The Points $(2, -6)$ And $(-9, 9)$?Show Your Work Here:Hint: To Add Infinity ($ ∞ \infty ∞ [/tex]), Type infinity.Enter Your Answer:

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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. It is a measure of how much the line rises (or falls) vertically for a given horizontal distance. The slope of a line can be calculated using the coordinates of two points on the line. In this article, we will explore how to find the slope of a line that passes through the points (2, -6) and (-9, 9).

What is Slope?

The slope of a line is a measure of how steep it is. 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 usually denoted by the letter 'm' and can be calculated using the following formula:

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

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

Finding the Slope of a Line

To find the slope of a line that passes through the points (2, -6) and (-9, 9), we can use the formula mentioned above. We will substitute the coordinates of the two points into the formula and calculate the slope.

Step 1: Identify the Coordinates of the Two Points

The coordinates of the two points are (2, -6) and (-9, 9). We will use these coordinates to calculate the slope.

Step 2: Substitute the Coordinates into the Formula

We will substitute the coordinates of the two points into the formula:

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

m = (9 - (-6)) / (-9 - 2)

Step 3: Simplify the Expression

We will simplify the expression by evaluating the subtraction and division:

m = (9 + 6) / (-9 - 2)

m = 15 / -11

Step 4: Calculate the Slope

We will calculate the slope by dividing 15 by -11:

m = -15/11

Conclusion

In this article, we explored how to find the slope of a line that passes through the points (2, -6) and (-9, 9). We used the formula m = (y2 - y1) / (x2 - x1) to calculate the slope and obtained a value of -15/11. The slope of a line is a fundamental concept in mathematics that helps us understand the steepness or incline of a line. It is a measure of how much the line rises (or falls) vertically for a given horizontal distance.

Frequently Asked Questions

  • What is the slope of a line? The slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
  • How do I calculate the slope of a line? To calculate the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
  • What is the formula for calculating the slope of a line? The formula for calculating the slope of a line is m = (y2 - y1) / (x2 - x1).

References

Related Articles

  • [1] How to Find the Equation of a Line
  • [2] How to Find the Slope of a Line Using the Point-Slope Form
  • [3] How to Find the Slope of a Line Using the Slope-Intercept Form

Introduction

In our previous article, we explored how to find the slope of a line that passes through two points. We used the formula m = (y2 - y1) / (x2 - x1) to calculate the slope and obtained a value of -15/11. In this article, we will answer some frequently asked questions about the slope of a line.

Q&A

Q: What is the slope of a line?

A: The slope of a line is a measure of how steep it is. 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 calculate the slope of a line?

A: To calculate the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

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

A: The formula for calculating the slope of a line is m = (y2 - y1) / (x2 - x1).

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

A: The slope of a line is a measure of how steep it is, while the y-intercept is the point where the line intersects the y-axis. The slope is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line, while the y-intercept is the value of y when x is equal to 0.

Q: Can the slope of a line be negative?

A: Yes, the slope of a line can be negative. A negative slope indicates that the line is sloping downward from left to right.

Q: Can the slope of a line be zero?

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

Q: Can the slope of a line be undefined?

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

Q: How do I determine the direction of a line based on its slope?

A: To determine the direction of a line based on its slope, you can use the following rules:

  • If the slope is positive, the line is sloping upward from left to right.
  • If the slope is negative, the line is sloping downward from left to right.
  • If the slope is zero, the line is horizontal.
  • If the slope is undefined, the line is vertical.

Q: How do I graph a line based on its slope and y-intercept?

A: To graph a line based on its slope and y-intercept, you can use the following steps:

  1. Plot the y-intercept on the graph.
  2. Use the slope to determine the direction of the line.
  3. Plot a point on the line that is one unit to the right of the y-intercept.
  4. Draw a line through the y-intercept and the point you plotted in step 3.

Conclusion

In this article, we answered some frequently asked questions about the slope of a line. We covered topics such as how to calculate the slope, what the formula for calculating the slope is, and how to determine the direction of a line based on its slope. We also covered how to graph a line based on its slope and y-intercept.

Frequently Asked Questions

  • What is the slope of a line?
  • How do I calculate the slope of a line?
  • What is the formula for calculating the slope of a line?
  • What is the difference between the slope and the y-intercept?
  • 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 determine the direction of a line based on its slope?
  • How do I graph a line based on its slope and y-intercept?

References

Related Articles

  • [1] How to Find the Equation of a Line
  • [2] How to Find the Slope of a Line Using the Point-Slope Form
  • [3] How to Find the Slope of a Line Using the Slope-Intercept Form