To graph the line represented by the equation \(y = 7x - 4\), you can follow these steps:
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Identify the slope and y-intercept:
- The slope (m) is 7.
- The y-intercept (b) is -4.
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Plot the y-intercept:
- Start by plotting the point where the line crosses the y-axis. The y-intercept is at the point (0, -4).
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Use the slope to find another point:
- The slope of 7 can be interpreted as the rise over run, or \(\frac{7}{1}\). This means that for every 1 unit you move to the right (run), you move up 7 units (rise).
- Starting from the y-intercept (0, -4), you can move right 1 unit to (1, -4) and then up 7 units to (1, 3). Therefore, another point on the line is (1, 3).
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Draw the line:
- Plot the two points (0, -4) and (1, 3) on the graph.
- Use a ruler to draw a straight line through these points. Extend the line in both directions.
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Label the line:
- Optionally, you can label the equation of the line \(y = 7x - 4\) next to it.
You can use graphing software or graph paper to create a visual representation if needed, but these steps will help you understand how to graph it manually!