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Relating the Graph of to its Slope and y-Intercept
By examining the graph of the linear equation , 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 , making the y-intercept . Furthermore, moving from one point to another on the line reveals a vertical rise of and a horizontal run of , resulting in a slope of . When we compare these graphical values to the original equation, we see that the coefficient of the term () corresponds exactly to the slope, and the constant term () 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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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Learn After
In the linear equation , specific values represent different features of the line's graph. Match each value from the equation with the graphical feature it identifies.
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