What Is The Slope Of A Line That Passes Through The Points { (-3,-5)$}$ And { (1,7)$}$ In The { Xy$}$-plane?Choose 1 Answer:A. 6B. 3C. { \frac{1}{2}$}$D. -1

Mar 8, 2025 by ADMIN 157 views

What is the Slope of a Line that Passes Through Two Given Points in the xy-Plane?

Introduction to Slope

The slope of a line is a fundamental concept in mathematics, particularly in geometry and algebra. It is a measure of how steep a line is and 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 two given points in the xy-plane.

What is Slope?

Slope is a numerical value that represents the rate of change of a 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 of a line can be positive, negative, or zero, depending on the direction and steepness of the line.

Formula for Slope

The formula for calculating the slope of a line that passes through two points (x1, y1) and (x2, y2) is:

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

where m is the slope of the line.

Example: Finding the Slope of a Line that Passes Through Two Given Points

Let's consider the problem of finding the slope of a line that passes through the points (-3, -5) and (1, 7) in the xy-plane.

Step 1: Identify the Coordinates of the Two Points

The coordinates of the two points are (-3, -5) and (1, 7).

Step 2: Apply the Formula for Slope

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

m = (7 - (-5)) / (1 - (-3)) m = (7 + 5) / (1 + 3) m = 12 / 4 m = 3

Step 3: Interpret the Result

The result of the calculation is a slope of 3, which means that the line passes through the two points with a steepness of 3 units of rise for every 1 unit of run.

Conclusion

In conclusion, the slope of a line that passes through the points (-3, -5) and (1, 7) in the xy-plane is 3. This can be calculated using the formula for slope, which is m = (y2 - y1) / (x2 - x1). The result of the calculation provides valuable information about the steepness and direction of the line.

Frequently Asked Questions

What is the slope of a line that passes through the points (2, 4) and (5, 6)? Using the formula for slope, we can calculate the slope of the line as follows: m = (6 - 4) / (5 - 2) m = 2 / 3 m = 2/3
What is the slope of a line that passes through the points (-2, 3) and (4, 5)? Using the formula for slope, we can calculate the slope of the line as follows: m = (5 - 3) / (4 - (-2)) m = 2 / 6 m = 1/3

Final Answer

The final answer is: B. 3

Introduction

In our previous article, we explored how to find the slope of a line that passes through two given points in the xy-plane. In this article, we will answer some frequently asked questions related to the slope of a line.

Q1: What is the slope of a line that passes through the points (2, 4) and (5, 6)?

A1: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (6 - 4) / (5 - 2) m = 2 / 3 m = 2/3

Q2: What is the slope of a line that passes through the points (-2, 3) and (4, 5)?

A2: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (5 - 3) / (4 - (-2)) m = 2 / 6 m = 1/3

Q3: What is the slope of a line that passes through the points (0, 0) and (3, 4)?

A3: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (4 - 0) / (3 - 0) m = 4 / 3 m = 4/3

Q4: What is the slope of a line that passes through the points (-5, 2) and (2, 6)?

A4: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (6 - 2) / (2 - (-5)) m = 4 / 7 m = 4/7

Q5: What is the slope of a line that passes through the points (1, 1) and (4, 4)?

A5: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (4 - 1) / (4 - 1) m = 3 / 3 m = 1

Q6: What is the slope of a line that passes through the points (-3, -2) and (2, 3)?

A6: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (3 - (-2)) / (2 - (-3)) m = 5 / 5 m = 1

Q7: What is the slope of a line that passes through the points (0, 0) and (0, 5)?

A7: To find the slope of the line, we can use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (5 - 0) / (0 - 0) m = 5 / 0 m = undefined

Conclusion

In conclusion, the slope of a line that passes through two given points can be calculated using the formula for slope, which is m = (y2 - y1) / (x2 - x1). The result of the calculation provides valuable information about the steepness and direction of the line.

Final Answer

The final answer is: B. 3