To determine the initial value and the rate of change of a linear function from a graph, follow these steps:
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Initial Value (y-intercept): The initial value of a linear function is the value of \( y \) when \( x = 0 \). Locate the point where the line intersects the \( y \)-axis. This point will provide the initial value.
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Rate of Change (slope): The rate of change (or slope) of a linear function can be calculated using the formula: \[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \] To find the slope, choose two clear points on the line (preferably with integer coordinates) and substitute the coordinates into the formula.
If you provide specific details from the graph, such as coordinates of points or the appearance of the graph, I can calculate the initial value and the rate of change for you!
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