To identify the slope and y-intercept of the linear equation \( y = -\frac{2}{3}x + 6 \), we begin with the general form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Identify the y-intercept (b): In the equation \( y = -\frac{2}{3}x + 6 \), the y-intercept \( b \) is 6. This means the graph of the line crosses the y-axis at the point \( (0, 6) \).
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Identify the slope (m): The slope \( m \) in this equation is \( -\frac{2}{3} \). This means that for every 3 units you move to the right (positive direction along the x-axis), the line will move down 2 units (negative direction along the y-axis).
Now, we can graph the equation:
Steps to Graph the Equation:
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Plot the y-intercept: Start by plotting the point \( (0, 6) \) on the graph.
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Use the slope to find another point: From the point \( (0, 6) \), use the slope \( -\frac{2}{3} \).
- Move 3 units to the right (to \( x = 3 \)).
- Move 2 units down (to \( y = 4 \)). This gives you the point \( (3, 4) \).
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Plot the second point: Plot the point \( (3, 4) \) on the graph.
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Draw the line: Connect the points \( (0, 6) \) and \( (3, 4) \) with a straight line, and extend it in both directions.
Summary:
- Slope: \( -\frac{2}{3} \)
- Y-intercept: \( 6 \)
- Points on the graph: \( (0, 6) \) and \( (3, 4) \)
The graph will show a straight line that slopes downward from left to right due to the negative slope.