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 point where the line crosses the y-axis. This point is \( (0, 1) \).
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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 (positive direction on the x-axis), you move 5 units up (positive direction on the y-axis).
- From the point \( (0, 1) \), move 6 units to the right to \( x = 6 \) and then 5 units up to \( y = 6 \). This gives you the point \( (6, 6) \).
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Draw the Line:
- Now that you have two points, \( (0, 1) \) and \( (6, 6) \), draw a straight line through these points. This line extends infinitely in both directions.
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Label the Axes:
- Make sure to label your axes (x-axis and y-axis) and mark the points that you plotted.
Your graph should show a straight line that slopes upwards from left to right, passing through the points you have identified.
If you want to visualize this graph, you could use a graphing tool or software to plot the points and draw the line, but the above instructions give you a good way to do it by hand as well!