To graph the equation \( y = \frac{5}{6}x + 1 \), follow these steps:
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Identify the slope and y-intercept: The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m = \frac{5}{6} \) and the y-intercept \( b = 1 \).
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Plot the y-intercept: Start by plotting the y-intercept on the graph. This occurs at the point \( (0, 1) \).
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Use the slope to find another point: The slope \( \frac{5}{6} \) means that for every 6 units you move to the right (along the x-axis), you move 5 units up (along the y-axis).
- From the point \( (0, 1) \), go right 6 units (to \( x = 6 \)) and up 5 units (to \( y = 6 \)). This gives you another point at \( (6, 6) \).
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Draw the line: Connect the points \( (0, 1) \) and \( (6, 6) \) with a straight line. Extend the line in both directions, adding arrows at both ends to indicate that it continues indefinitely.
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Label: You may want to label the axes and provide a title for the graph for clarity.
This will give you a visual representation of the equation \( y = \frac{5}{6}x + 1 \). If you were to plot more points, you could do so by selecting additional values for \( x \) and calculating their corresponding \( y \) values using the equation. For instance:
- If \( x = 0 \), then \( y = 1 \)
- If \( x = 6 \), then \( y = 6 \)
- If \( x = 12 \), then \( y = 11 \)
- If \( x = -6 \), then \( y = -4 \)
This will provide further points to ensure your line is accurate.