## y = 2x + 1

### The equation y = 2x + 1 represents a linear function

The equation y = 2x + 1 represents a linear function. In this equation, y is the dependent variable and x is the independent variable. The coefficient 2 represents the slope of the line, which determines how steep the line goes upward or downward.

To understand the equation better, let’s analyze it step by step:

1. The constant term 1 is added to the equation. This means that when x equals 0, y will be 1. So, the point (0, 1) lies on the line.

2. The coefficient 2 indicates that for every 1 unit increase in x, y will increase by 2 units. If x equals 1, then y will be 3 (2(1) + 1). Thus, the point (1, 3) also lies on the line.

3. Similarly, for every 1 unit decrease in x, y will decrease by 2 units. For example, if x equals -1, then y will be -1 (2(-1) + 1). So, the point (-1, -1) lies on the line.

Based on these observations, we can plot the line by connecting these points (0, 1), (1, 3), and (-1, -1). Since the slope is positive (2), the line will be upward sloping, passing through the points.

In conclusion, the equation y = 2x + 1 represents a linear function with a slope of 2 and a y-intercept of 1.

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