Discover the Sleek Slope of MN: M(1, 3) & N(5, 0) in a Geo-Trek!

The slope of the line MN, which contains points M(1, 3) and N(5, 0), can be calculated using the formula (change in y)/(change in x).

Are you curious to find out the slope of line MN? Well, let's delve into the world of coordinates and geometry to unravel this mystery. The line MN is formed by connecting two points, M(1, 3) and N(5, 0). Now, how can we determine the slope of this line? By using the magical power of mathematics, we can calculate it with precision and uncover the secrets hidden within these coordinates. So, sit back, relax, and let's embark on this mathematical journey together!

Introduction

In the field of mathematics, the concept of slope plays a crucial role in understanding the characteristics and behavior of lines. In this article, we will explore the slope of a line that contains two given points, M(1, 3) and N(5, 0). By understanding the process of finding the slope, we can gain valuable insights into the relationship between these two points.

Defining Slope

Slope is a measure of how steep or inclined a line is. It provides us with information about the rate of change between two points on a line. The slope of a line is represented by the letter 'm' and can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

This formula allows us to determine the slope of any line, provided we know the coordinates of two distinct points on that line.

Identifying the Coordinates

Before we can calculate the slope of line MN, we need to identify the coordinates of the two given points, M(1, 3) and N(5, 0). These coordinates represent the x and y values that define the position of each point in a two-dimensional plane.

Calculating the Difference in Y-Coordinates

To find the slope of line MN, we need to calculate the difference in y-coordinates between the two given points, M and N. In this case, the y-coordinate of point M is 3, while the y-coordinate of point N is 0.

y₂ - y₁ = 0 - 3 = -3

Calculating the Difference in X-Coordinates

Similarly, we also need to calculate the difference in x-coordinates between the two points, M and N. The x-coordinate of point M is 1, while the x-coordinate of point N is 5.

x₂ - x₁ = 5 - 1 = 4

Applying the Slope Formula

Now that we have determined the differences in both the y and x coordinates, we can substitute these values into the slope formula to find the slope of line MN.

m = (-3) / 4

Reducing the Slope

To simplify the slope, we can reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.

m = -3 / 4

Interpreting the Slope

The resulting slope of -3/4 can be interpreted as follows: for every four units we move to the right along the x-axis, the line goes down by three units along the y-axis. This negative slope indicates a downward trend, suggesting that as x increases, y decreases.

Conclusion

In summary, the slope of line MN, which contains the points M(1, 3) and N(5, 0), is -3/4. By utilizing the slope formula and calculating the differences in y and x coordinates, we were able to determine this important characteristic of the line. Understanding the slope provides us with valuable information about the relationship between the two given points and the behavior of the line connecting them.

Introduction

Explaining the concept of slope and its importance in understanding the relationship between two points on a line.

When studying lines in mathematics, one crucial concept to grasp is the slope. Slope represents the steepness or the inclination of a line and provides valuable information about the relationship between two points on that line. By calculating the slope, we can determine how the line is changing as it moves from one point to another. In this explanation, we will explore how to calculate the slope of a line using the coordinates of two given points, M(1, 3) and N(5, 0), on the line MN.

Two given points

Describing the coordinates of points M(1, 3) and N(5, 0) on the line MN.

Let's start by identifying the coordinates of the two given points on the line MN. Point M is located at (1, 3), meaning its x-coordinate is 1 and its y-coordinate is 3. Similarly, point N is located at (5, 0), with an x-coordinate of 5 and a y-coordinate of 0. These points represent specific positions on the line MN, and by analyzing them, we can determine the slope of the line.

Calculating the change in y

Showing how to subtract the y-coordinates of the two points to find the change in vertical position.

To calculate the slope, we need to determine the change in the vertical position between the two points. This is done by subtracting the y-coordinate of one point from the y-coordinate of the other. In our case, we subtract the y-coordinate of point M (3) from the y-coordinate of point N (0). Thus, the change in y is 0 - 3 = -3.

Calculating the change in x

Demonstrating how to subtract the x-coordinates of the two points to find the change in horizontal position.

Similarly, we need to calculate the change in the horizontal position between the two points. This is achieved by subtracting the x-coordinate of one point from the x-coordinate of the other. In our example, we subtract the x-coordinate of point M (1) from the x-coordinate of point N (5). Thus, the change in x is 5 - 1 = 4.

Slope formula

Introducing the formula for calculating slope, which is the change in y divided by the change in x.

Now that we have determined the changes in both the vertical and horizontal positions, we can calculate the slope. The slope is obtained by dividing the change in y by the change in x. In mathematical terms, the slope is given by the formula:

slope = (change in y) / (change in x)

Applying the formula

Plugging in the values obtained in steps 3 and 4 into the slope formula.

Let's apply the slope formula to our example. We already found that the change in y is -3 and the change in x is 4. By substituting these values into the formula, we get:

slope = (-3) / (4)

Simplifying the equation

Showing how to simplify the slope equation by dividing the values obtained in step 6.

To simplify the equation, we divide the numerator (-3) by the denominator (4). The result is:

slope = -3/4

Interpretation

Explaining what the slope represents – the rate of change in the vertical direction for every unit change in the horizontal direction.

The slope we calculated, -3/4, represents the rate of change in the vertical direction for every unit change in the horizontal direction. In other words, for every increase of 1 in the x-coordinate, the y-coordinate decreases by 3/4. This negative slope indicates that the line MN is decreasing as it moves from left to right.

Calculation result

Providing the calculated value of the slope for the line MN using the coordinates of points M(1, 3) and N(5, 0).

After performing the calculations, we determined that the slope of the line MN, using the coordinates M(1, 3) and N(5, 0), is -3/4.

Conclusion

Summarizing the main points discussed and highlighting the significance of the slope in describing the relationship between the two points on the line MN.

The slope plays a crucial role in understanding the relationship between two points on a line. By calculating the slope, we can determine the steepness and direction of the line, providing valuable insights into its behavior. In this explanation, we utilized the coordinates of points M(1, 3) and N(5, 0) to calculate the slope of the line MN. The resulting slope of -3/4 indicates a decrease in the y-coordinate for every unit increase in the x-coordinate. Understanding the slope allows us to comprehend the rate of change and visualize the line's characteristics.

When determining the slope of a line, we need to consider the coordinates of two points on the line. In this case, the line contains the points M(1, 3) and N(5, 0). Let's calculate the slope of line MN using the formula:

Slope (m) = (change in y) / (change in x)

1. Identify the change in y: The y-coordinate of point N is 0, while the y-coordinate of point M is 3. Therefore, the change in y is 0 - 3 = -3.
2. Identify the change in x: The x-coordinate of point N is 5, while the x-coordinate of point M is 1. Therefore, the change in x is 5 - 1 = 4.
3. Calculate the slope: Divide the change in y by the change in x. In this case, -3 / 4 = -0.75.

Therefore, the slope of line MN is -0.75. This means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 0.75 units. The negative sign indicates that the line slopes downwards from left to right.

Thank you for visiting our blog! Today, we are going to discuss an interesting topic in mathematics - the slope of a line. Specifically, we will be exploring the slope of the line segment MN, which is formed by two points M(1, 3) and N(5, 0). So, without further ado, let's dive into the world of slopes and discover the answer to our question!

To find the slope of the line segment MN, we can use the formula: slope = (change in y-coordinates)/(change in x-coordinates). In other words, we need to determine how much the y-coordinate changes as we move from point M to point N, and divide it by the change in the x-coordinate. Let's calculate it step by step.

First, let's determine the change in the y-coordinates. The y-coordinate of point M is 3, and the y-coordinate of point N is 0. Therefore, the change in the y-coordinates is 0 - 3 = -3. Now, let's determine the change in the x-coordinates. The x-coordinate of point M is 1, and the x-coordinate of point N is 5. Thus, the change in the x-coordinates is 5 - 1 = 4. Finally, we can calculate the slope by dividing the change in y-coordinates (-3) by the change in x-coordinates (4), giving us a slope of -3/4.

In conclusion, the slope of the line segment MN, formed by the points M(1, 3) and N(5, 0), is -3/4. Understanding slopes is crucial in various fields, such as physics, engineering, and even everyday life. It helps us analyze the steepness or inclination of lines, allowing us to make predictions, solve problems, and gain insights. We hope you found this article informative and that it has deepened your understanding of slopes. Thank you once again for visiting our blog, and we look forward to sharing more mathematical concepts with you in the future!

What Is the Slope of Line MN?

People Also Ask:

• How do you find the slope of a line?
• What are the coordinates of points M and N?
• Why is slope important in mathematics?

Explanation:

To find the slope of a line, we use the formula: slope = (change in y-coordinates) / (change in x-coordinates).

Step 1:

Identify the coordinates of points M and N.

Point M has coordinates (1, 3), where x₁ = 1 and y₁ = 3.

Point N has coordinates (5, 0), where x₂ = 5 and y₂ = 0.

Step 2:

Calculate the change in y-coordinates and change in x-coordinates.

Change in y-coordinates (Δy) = y₂ - y₁ = 0 - 3 = -3.

Change in x-coordinates (Δx) = x₂ - x₁ = 5 - 1 = 4.

Step 3:

Substitute the values into the slope formula.

slope = Δy / Δx = -3 / 4 = -0.75.

Answer:

The slope of line MN, which passes through points M(1, 3) and N(5, 0), is -0.75.

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