To derive the equation of a line in slope-intercept form (y = mx + b), we need to identify the slope (m) and the y-intercept (b) from the graph.
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Finding the Slope (m): The slope is calculated as the change in y divided by the change in x (rise over run). Look for two distinct points on the line, for example, (x1, y1) and (x2, y2), and use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
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Finding the Y-Intercept (b): This is the value of y when x is 0. Locate where the line crosses the y-axis.
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Creating the Equation: Once you have the slope and y-intercept, substitute those values into the slope-intercept form equation: \[ y = mx + b \]
If you can provide more specific information about the graph, such as the coordinates of points or the behavior of the line, I could help derive the equation more accurately.