To answer the questions based on the graph, I would need specific details from the graph itself, such as the coordinates of points, the value of the y-intercept, the rise over run for the slope, and the overall appearance of the line to derive its equation. However, I can guide you on how to determine the required values.
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Y-intercept: This is the point where the line crosses the y-axis. You can usually find this value by checking the y-coordinate of the point where the line intersects the y-axis.
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Slope: The slope \( m \) of a line is determined by the formula: \[ m = \frac{{\text{rise}}}{{\text{run}}} \] Choose two points on the line and calculate the difference in y-coordinates (rise) and the difference in x-coordinates (run).
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Equation of the line in slope-intercept form: The slope-intercept form is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. Insert the slope and y-intercept into this formula.
To answer your specific inputs:
- For the y-intercept, input the value you find from the graph.
- For the slope, input the value based on your rise and run calculations.
- For the equation of the line, use the selected equation if it fits the slope and the y-intercept you've found, or calculate it yourself based on the values you determined.
The provided response, "y = 1/2x + 2," suggests that the slope \( m \) is 1/2 and the y-intercept \( b \) is 2. Ensure these align with your calculations based on the graph. If you have any specific coordinates or additional details from the graph, I can provide further guidance!