graph y 2x 7

Guri Bee

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17-10-2024

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Graphing the Line y = 2x + 7: A Step-by-Step Guide

Understanding how to graph linear equations is a fundamental skill in mathematics. Let's explore how to graph the line represented by the equation y = 2x + 7.

Understanding the Equation

The equation y = 2x + 7 is in slope-intercept form, which is written as y = mx + c, where:

• m represents the slope of the line. In our equation, m = 2, indicating that for every 1 unit increase in x, y increases by 2 units.
• c represents the y-intercept, the point where the line crosses the y-axis. In our equation, c = 7, meaning the line intersects the y-axis at the point (0, 7).

Steps to Graph the Line

1. Plot the y-intercept: Begin by marking the point (0, 7) on your graph.

2. Use the slope to find another point: The slope of 2 can be expressed as 2/1. This means that for every 1 unit you move to the right on the x-axis, you must move 2 units up on the y-axis. Starting from the y-intercept, move 1 unit to the right and 2 units up. Plot this new point.

3. Draw the line: Connect the two plotted points with a straight line. This line represents the graph of the equation y = 2x + 7.

Additional Notes

• You can use the slope to find as many points on the line as you need.
• To plot the graph accurately, you can use graph paper or a graphing tool like Desmos.

Example

Let's use the equation y = 2x + 7 to find a few points and confirm our understanding:

• When x = 1, y = 2(1) + 7 = 9. So, the point (1, 9) lies on the line.
• When x = -2, y = 2(-2) + 7 = 3. So, the point (-2, 3) lies on the line.

Conclusion

By understanding the slope-intercept form and applying the steps outlined above, you can easily graph linear equations like y = 2x + 7. This fundamental skill is essential for understanding linear relationships and solving problems in various fields, from physics to economics.

Attribution:

While this article has been written by the author, it draws inspiration and utilizes the concepts of graphing linear equations found in numerous online resources, including Github repositories. The specific information regarding slope and y-intercept is commonly discussed in these repositories, and the process of graphing is generally understood and shared across various platforms.