Line { AB $}$ Contains Points { A(4,5) $}$ And { B(9,7) $}$. What Is The Slope Of { \overleftrightarrow{AB}$}$?A. { -\frac{5}{2}$}$ B. { -\frac{2}{5}$}$ C. { \frac{2}{5}$}$ D.

by ADMIN 179 views

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 over a given horizontal distance. In this article, we will explore the concept of slope and how to calculate it using the coordinates of two points on a line.

What is Slope?

The slope of a line is denoted by the letter 'm' and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It can be calculated using the formula:

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

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

Calculating the Slope of Line AB

In this problem, we are given two points on line AB: A(4, 5) and B(9, 7). We need to calculate the slope of line AB using the coordinates of these two points.

Step 1: Identify the Coordinates

The coordinates of point A are (4, 5) and the coordinates of point B are (9, 7).

Step 2: Apply the Slope Formula

Using the slope formula, we can calculate the slope of line AB as follows:

m = (y2 - y1) / (x2 - x1) = (7 - 5) / (9 - 4) = 2 / 5

Step 3: Simplify the Fraction

The fraction 2/5 is already in its simplest form, so we can write the slope of line AB as:

m = 2/5

Conclusion

In this article, we have learned how to calculate the slope of a line using the coordinates of two points on the line. We have applied the slope formula to find the slope of line AB, which is 2/5. This concept is essential in mathematics and is used in various applications, including geometry, algebra, and calculus.

Slope Formula: A Review

The slope formula is a fundamental concept in mathematics that helps us calculate the slope of a line. It is used to find the steepness or incline of a line and is essential in various applications. The formula is:

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

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

Example Problems

Here are a few example problems to help you practice calculating the slope of a line:

  • Find the slope of line PQ, given points P(2, 3) and Q(5, 6).
  • Find the slope of line RS, given points R(1, 2) and S(4, 5).
  • Find the slope of line TU, given points T(3, 4) and U(6, 7).

Practice Problems

Here are a few practice problems to help you practice calculating the slope of a line:

  • Find the slope of line VW, given points V(2, 3) and W(5, 6).
  • Find the slope of line XY, given points X(1, 2) and Y(4, 5).
  • Find the slope of line ZA, given points Z(3, 4) and A(6, 7).

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most 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 much the line rises (or falls) vertically over a given horizontal distance. 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 need to use the slope 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 difference between a positive and negative slope?

A: A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

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 at all.

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 horizontal change (run).

Q: How do I determine the slope of a line from a graph?

A: To determine the slope of a line from a graph, you need to identify two points on the line and calculate the slope using the slope formula.

Q: Can I use the slope formula to find the equation of a line?

A: Yes, you can use the slope formula to find the equation of a line. Once you have the slope and one point on the line, you can use the point-slope form of a linear equation to find the equation of the line.

Q: What is the point-slope form of a linear equation?

A: The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Q: Can I use the slope formula to find the equation of a line in slope-intercept form?

A: Yes, you can use the slope formula to find the equation of a line in slope-intercept form. Once you have the slope and one point on the line, you can use the slope-intercept form of a linear equation to find the equation of the line.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is:

y = mx + b

where m is the slope of the line and b is the y-intercept of the line.

Conclusion

In this article, we have answered some of the most frequently asked questions about the slope of a line. We have covered topics such as calculating the slope of a line, determining the slope of a line from a graph, and using the slope formula to find the equation of a line. We hope that this article has been helpful in clarifying any questions you may have had about the slope of a line.