y=-2x graph

2025

2 min read 31-03-2025

The equation y = -2x represents a fundamental concept in algebra: a linear equation. This guide will explore its characteristics, plotting techniques, and real-world applications. Understanding this seemingly simple equation provides a strong foundation for grasping more complex mathematical concepts.

What Does y = -2x Mean?

The equation y = -2x is a linear equation, meaning its graph is a straight line. It shows a relationship between two variables, x and y, where y is always twice the value of x, but with a negative sign. This negative sign indicates an inverse relationship; as x increases, y decreases, and vice versa.

Key Characteristics of y = -2x

Linearity: The equation is linear because the highest power of x is 1.
Slope: The slope of the line is -2. This means for every 1 unit increase in x, y decreases by 2 units. The negative slope signifies a downward trend from left to right.
y-intercept: The y-intercept is 0. This means the line passes through the origin (0,0) on the coordinate plane.

How to Graph y = -2x

There are several ways to graph this equation:

Method 1: Using the Slope and y-intercept

Plot the y-intercept: Since the y-intercept is 0, plot a point at the origin (0,0).
Use the slope: The slope is -2, which can be written as -2/1. This means a rise of -2 and a run of 1. From the origin (0,0), move 1 unit to the right and 2 units down to plot another point (1,-2).
Draw the line: Draw a straight line through the two points you've plotted. This line represents the graph of y = -2x.

Method 2: Creating a Table of Values

Create a table with x and y values:

x	y = -2x
-2	4
-1	2
0	0
1	-2
2	-4

Plot these points on a coordinate plane and connect them with a straight line.

Real-World Applications of y = -2x

While seemingly simple, the concept of y = -2x appears in various real-world scenarios:

Linear Depreciation: The value of an asset decreasing at a constant rate can be modeled using a linear equation similar to y = -2x. Here, x could represent time, and y the remaining value.
Constant Rate of Change: Any situation involving a constant rate of decrease can be represented. For example, water draining from a tank at a consistent rate.
Physics: In physics, many relationships are linear, with a negative slope indicating an inverse relationship between variables.

Frequently Asked Questions (FAQs)

Q: What is the slope of the line y = -2x?

A: The slope is -2.

Q: Where does the line y = -2x intersect the y-axis?

A: The line intersects the y-axis at the origin (0,0).

Q: Is y = -2x a function?

A: Yes, y = -2x is a function because for every x value, there is only one corresponding y value.

Q: How can I find points on the line y = -2x other than those shown in the table?

A: Substitute any x-value into the equation to calculate the corresponding y-value. For instance, if x = 3, then y = -2(3) = -6. The point (3, -6) lies on the line.

Conclusion

The graph of y = -2x is a simple yet powerful representation of a linear relationship. By understanding its characteristics and plotting techniques, you gain a fundamental understanding of linear equations and their various applications in diverse fields. Remember, mastering this basic concept is a crucial stepping stone to tackling more advanced mathematical problems.