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.
More Answers:
Understanding Linear Relationships | Exploring the Equation y = 4x and its GraphUnderstanding Linear Functions | Exploring the Equation y = -2x and its Slope and Y-Intercept
Understanding the Linear Equation y = x + 2 | Graphing, Intercepts, and Interpretation