Graph of y = 2x + 1
Interactive graph of y = 2x + 1 (linear equation). Explore slope-intercept form, the meaning of slope and y-intercept with our graphing calculator.
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Understanding the Function
The function y = 2x + 1 is a linear equation in slope-intercept form y = mx + b, where the slope m = 2 and the y-intercept b = 1. The line crosses the y-axis at (0, 1) and rises 2 units for every 1 unit increase in x, making it steeper than the identity line y = x.
Linear functions are the foundation of algebra and appear throughout science and engineering. The slope represents the rate of change, while the y-intercept represents the starting value. In physics, a linear relationship between distance and time indicates constant velocity; in economics, a linear cost function implies constant marginal cost.
Key properties: slope of 2, y-intercept at (0, 1), x-intercept at (-1/2, 0), domain and range are both all real numbers. The function is increasing everywhere with a constant rate of change. The derivative is 2, and the integral is x² + x + C.