Discover the Captivating Slope of Line AB with Points A(4, 5) and B(9, 7)!
Are you curious about the slope of Line AB that contains the points A(4, 5) and B(9, 7)? Well, allow me to enlighten you! The slope of a line is a measure of its steepness, indicating how much the y-coordinate changes for every unit increase in the x-coordinate. By determining the slope of Line AB, we can gain valuable insights into its direction and characteristics. So, let's dive in and uncover the slope of this intriguing line!
Introduction
In the field of mathematics, understanding the concept of slope is crucial. It helps us measure the steepness or inclination of a line and provides valuable information about its characteristics. In this article, we will focus on a specific line, AB, formed by two given points A(4, 5) and B(9, 7). Our main objective is to determine the slope of this line and understand its significance.
Understanding Slope
Slope is a fundamental concept in mathematics that measures the rate at which a line rises or falls as it moves horizontally. It is represented by the letter 'm' and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. The slope can be positive, negative, zero, or undefined, depending on the line's characteristics.
Calculating the Slope of Line AB
To calculate the slope of line AB, we will use the given points A(4, 5) and B(9, 7) in the slope formula. Let's substitute the values into the formula:
m = (7 - 5) / (9 - 4)
m = 2 / 5
Therefore, the slope of line AB is 2/5.
Interpreting the Slope
Now that we have determined the slope of line AB, let's interpret its meaning. The slope of 2/5 tells us that for every unit increase in the horizontal direction (x-axis), the line rises by 2/5 units in the vertical direction (y-axis).
Positive Slope
Since the slope is positive, it indicates that the line AB is increasing from left to right. In other words, as we move towards the right on the x-axis, the y-values of the line increase.
Inclination and Steepness
The magnitude of the slope also provides information about the inclination or steepness of the line. A larger slope indicates a steeper line, while a smaller slope represents a less steep line. In this case, a slope of 2/5 suggests a moderate incline for line AB.
Graphical Representation
Let's visualize line AB on a graph to further understand its characteristics. By plotting points A(4, 5) and B(9, 7) on a coordinate plane, we can draw the line connecting these two points.
Coordinate Plane
A coordinate plane consists of an x-axis and a y-axis, forming four quadrants. The x-axis represents the horizontal values, while the y-axis represents the vertical values. The origin, denoted by (0, 0), lies at the intersection of these two axes.
Plotting Points A and B
Using the given coordinates A(4, 5) and B(9, 7), we locate point A at (4, 5) and point B at (9, 7) on the coordinate plane.
Drawing Line AB
Once the points are plotted, we can draw a straight line passing through A and B. This line represents line AB, which has a slope of 2/5.
Conclusion
In conclusion, the slope of line AB, formed by points A(4, 5) and B(9, 7), is 2/5. This tells us that for every unit increase in the horizontal direction, the line rises by 2/5 units in the vertical direction. Additionally, the positive slope indicates an increasing line from left to right. By understanding the concept of slope and its calculation, we can analyze lines and gain valuable insights about their characteristics.
Introduction to Line AB
In this section, we will provide an overview of Line AB, which contains points A(4, 5) and B(9, 7). Line AB is a straight line that passes through these two specific points on the coordinate plane.
Definition of Slope
Slope refers to the steepness or inclination of a line. It measures how much a line rises or falls as it moves horizontally. In other words, slope quantifies the rate at which the y-coordinates change with respect to the x-coordinates along the line.
Identifying Points A and B
Points A(4, 5) and B(9, 7) are the two coordinates that define Line AB. Point A has the coordinates (4, 5), where the x-coordinate is 4 and the y-coordinate is 5. Point B, on the other hand, has the coordinates (9, 7), with an x-coordinate of 9 and a y-coordinate of 7.
Calculation of Change in Y and Change in X
To calculate the change in y-coordinates and x-coordinates between points A and B, we subtract the initial y-coordinate from the final y-coordinate and the initial x-coordinate from the final x-coordinate, respectively. For Line AB, the change in y (Δy) is 7 - 5 = 2, and the change in x (Δx) is 9 - 4 = 5.
Definition of Slope Formula
The slope formula provides a mathematical equation to determine the slope of a line. It is expressed as: slope = Δy / Δx, where Δy represents the change in y-coordinates and Δx represents the change in x-coordinates between two points on the line.
Application of Slope Formula to Line AB
To find the slope of Line AB, we will substitute the values we calculated earlier into the slope formula. Therefore, slope = 2 / 5.
Calculation of Numerator and Denominator
The numerator of the slope formula is the change in y-coordinates, which is 2 in this case. The denominator represents the change in x-coordinates, which is 5. Thus, the slope of Line AB can be expressed as a fraction: 2/5.
Simplifying the Fraction
To simplify the fraction 2/5, we divide both the numerator and denominator by their greatest common divisor, which is 1 in this case. The simplified fraction remains 2/5.
Interpretation of Slope
The slope value of 2/5 indicates that for every 1 unit increase in the x-coordinate, the corresponding y-coordinate increases by 2/5 units. This means that Line AB has a moderate positive slope, indicating an upward trend as the x-coordinate increases.
Conclusion
In conclusion, the slope of Line AB, containing points A(4, 5) and B(9, 7), is 2/5. This signifies a moderate positive slope, indicating an upward trend as we move along the line from left to right on the coordinate plane.
When considering the line that contains points A(4, 5) and B(9, 7), we can determine its slope by utilizing the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
In this case, the change in y-coordinates is equal to the difference between the y-values of the two given points, which is 7 - 5 = 2. Similarly, the change in x-coordinates is equal to the difference between the x-values, which is 9 - 4 = 5.
Therefore, the slope of the line AB can be calculated as:
slope = (2)/(5)
This fraction cannot be simplified any further, so the slope is:
slope = 2/5
Therefore, the slope of the line AB is 2/5.
To summarize:
- The change in y-coordinates is 2.
- The change in x-coordinates is 5.
- The slope is calculated as 2/5.
Thank you for visiting our blog and taking the time to read our article on the slope of line AB, which contains points A(4, 5) and B(9, 7). In this closing message, we would like to summarize the key points discussed in the article and provide some final thoughts on the topic.
In the article, we explained that the slope of a line can be calculated using the formula (change in y)/(change in x). By applying this formula to the given points A(4, 5) and B(9, 7), we determined that the slope of line AB is 2/5.
Understanding the slope of a line is important in various fields, such as mathematics, physics, and engineering. It represents the rate at which the line is rising or falling, and it can be used to analyze trends, make predictions, and solve real-world problems.
Knowing the slope of a line allows us to determine whether the line is steep or gradual. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. A slope of zero means the line is horizontal. By interpreting the slope, we can gain valuable insights into the behavior and characteristics of the line.
In conclusion, the slope of line AB, which contains points A(4, 5) and B(9, 7), is 2/5. We hope this article has provided you with a clear understanding of how to calculate the slope of a line and its significance in various fields. Thank you once again for visiting our blog, and we look forward to sharing more informative content with you in the future.
People Also Ask about Line AB Contains Points A(4, 5) and B(9, 7)
1. What is the slope of line AB?
The slope of a line is a measure of how steep or slanted it is. To find the slope of line AB, we can use the formula:
Slope (m) = (change in y-coordinates) / (change in x-coordinates)
Let's calculate the slope of line AB using the coordinates of points A(4, 5) and B(9, 7):
- Identify the change in y-coordinates: 7 - 5 = 2
- Identify the change in x-coordinates: 9 - 4 = 5
- Divide the change in y-coordinates by the change in x-coordinates:
Slope (m) = 2/5 = 0.4
Therefore, the slope of line AB is 0.4.