Example

Relating the Graph of y=12x+3y = \frac{1}{2}x + 3 to its Slope and y-Intercept

By examining the graph of the linear equation y=12x+3y = \frac{1}{2}x + 3, we can directly identify its slope and y-intercept and relate them back to the equation. Observing the graph, the line crosses the y-axis at (0,3)(0, 3), making the y-intercept 33. Furthermore, moving from one point to another on the line reveals a vertical rise of 11 and a horizontal run of 22, resulting in a slope of m=12m = \frac{1}{2}. When we compare these graphical values to the original equation, we see that the coefficient of the xx term (12\frac{1}{2}) corresponds exactly to the slope, and the constant term (33) matches the y-coordinate of the y-intercept. This demonstrates the fundamental relationship between a linear equation and its graphical features.

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Updated 2026-05-03

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