To determine the rate of change (slope \( m \)) and the equation of a linear function based on a graph, we need the coordinates of at least two points from the graph.
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Rate of Change (Slope): The slope \( m \) can be calculated using the formula: \[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the values from two points on the graph (for example, \( (x_1, y_1) \) and \( (x_2, y_2) \)) to find the slope.
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Equation of the Line: Once the slope is determined, the equation of the line can be expressed in the slope-intercept form: \[ y = mx + b \] Here \( b \) is the y-intercept, which is the value of \( y \) when \( x = 0 \). You can find \( b \) from the graph where the line crosses the y-axis or calculate it after determining the slope using a known point.
If you provide specific points or values from the graph, I can help you calculate the rate of change and the equation.