Stepβbyβstep analysis of linear functions \( f(x) = mx + b \). Find slope, y-intercept, determine if increasing/decreasing, and visualize the relationship between rise and run on the graph.
π Interactive Calculator β’ Purple Theme β’ Linear Functions
β¨ A linear function is written as \( f(x) = mx + b \) where \( m \) is the slope (rate of change) and \( b \) is the y-intercept.
The slope tells us whether the function increases (positive slope) or decreases (negative slope). The graph below shows the line, the rise \( \Delta y \) and run \( \Delta x \).
\( f(x) = 2x - 3 \)
π Step-by-Step Analysis
STEP 1: Identify slope and y-intercept
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STEP 2: Determine if function increases or decreases
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STEP 3: Verify rise = slope Γ run on the graph
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π Graph of the Linear Function Green line: \( f(x) \) | Red points and segments show rise and run.
Adjust axis scale to see rise/run relationship clearly.