Master Julia Programming with a Tutorly Teaching Sample

Table of Contents

1. Introduction
2. Understanding the Problem
3. The Equation of a Straight Line
4. Finding the Y-Intercept
5. Analyzing the Slope
6. Graphing the Points
7. Writing the Final Equation
8. Evaluating the Answer Choices
9. Applying the Process of Elimination
10. Conclusion

Introduction

In this article, we will Delve into the topic of finding a point on a line in the x-y plane. We will explore the concepts involved in determining the equation of a straight line and utilizing slope and y-intercept. By breaking down the problem into smaller parts, we will demonstrate a step-by-step approach to arrive at the correct answer. So, let's get started and enhance our understanding of working with lines in the x-y plane.

1. Understanding the Problem

The initial step involves comprehending the problem statement and identifying its key components. In this particular problem, We Are given a line passing through the origin in the x-y plane with a slope of 1/7. Our objective is to determine which of the given points lies on this line. By applying our knowledge of equations of straight lines, we can effectively approach and solve this problem.

2. The Equation of a Straight Line

To begin, let's refresh our understanding of the general equation of a straight line in the x-y plane. The equation takes the form of y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept. By substituting the particular values provided in the problem, we can derive the equation that describes the given line accurately.

3. Finding the Y-Intercept

As the line passes through the origin (0, 0), it is crucial to determine the value of the y-intercept. The y-intercept denotes the point where the line intersects the y-axis. Since the x-coordinate at the origin is zero, we can deduce that the y-intercept is also zero. Understanding this fundamental aspect further assists us in formulating the correct equation for the line.

4. Analyzing the Slope

The next aspect we need to consider is the slope of the line. The problem provides us with a slope of 1/7. To gain a deeper understanding of the slope's significance, let us interpret it as the ratio of rise over run. In other words, for every one unit we move upwards on the graph, we need to move seven units to the right, as the slope is positive. By visualizing this relationship on the graph, we can identify additional points on the line.

5. Graphing the Points

Based on the slope calculation, we can plot additional points on the line. Starting from the origin, we move one unit up and seven units to the right, resulting in the point (7, 1). By connecting the origin and this new point, we can accurately draw the line that represents the given equation. Ensure to label the new point correctly for reference.

6. Writing the Final Equation

Now that we have both the y-intercept, which is zero, and the slope, which is 1/7, we can proceed to construct the final equation for the line. Substituting these values into the general equation of a straight line, we obtain y = (1/7)x. This equation represents the line passing through the origin with the specified slope.

7. Evaluating the Answer Choices

To determine which of the given points lies on the line, we can simply substitute the x-coordinate of each point into the equation and check if the resulting y-coordinate matches the corresponding answer choice. By systematically evaluating each answer choice, we can single out the correct point that lies on the line.

8. Applying the Process of Elimination

Using the process of elimination, we can narrow down our options and confirm the correct answer. By plugging in the x-coordinate from each answer choice into the equation, we observe that only the point (14, 2) satisfies the equation. This confirms that the point (14, 2) lies on the line with the equation y = (1/7)x.

9. Conclusion

In conclusion, we have successfully approached and solved the problem of finding a point on a line in the x-y plane. By understanding the key concepts of the y-intercept, slope, and the general equation of a straight line, we have effectively applied our knowledge to arrive at the correct answer. Remembering these fundamental principles will assist You in any future challenges involving lines in the x-y plane.

Highlights

• Understanding the key components of a line in the x-y plane.
• Applying the general equation of a straight line.
• Finding the y-intercept and analyzing the slope.
• Plotting points on the graph and drawing the line.
• Evaluating answer choices and utilizing the process of elimination.

FAQ

Q: Can the line in the x-y plane pass through any other point apart from the origin? A: Yes, a line in the x-y plane can pass through any point. In this specific problem, the line was required to pass through the origin.

Q: What happens if the slope of the line is negative? A: If the slope of the line is negative, it means that as we move horizontally to the right, the line will slope downwards.

Q: Is it necessary for the line to cross the x-axis? A: No, the line may or may not intersect the x-axis. It depends on the slope and the position of the y-intercept.

Q: How do we determine the y-intercept when the line does not pass through the origin? A: In such cases, the y-intercept is the y-coordinate of the point where the line intersects the y-axis.

Q: Can we find more points on the line using different values of x? A: Yes, we can find additional points on the line by substituting different values of x into the equation and solving for y.