To identify the slope and y-intercept from the equation \( y = -\frac{2}{3}x + 5 \), we can break it down:
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Slope (m): The slope is the coefficient of \( x \) in the equation. For the given equation: \[ m = -\frac{2}{3} \]
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Y-intercept (b): The y-intercept is the constant term in the equation. From the equation, we have: \[ b = 5 \]
Now, we can summarize:
- Y-intercept: \( (0, 5) \)
- Slope: \( -\frac{2}{3} \)
Graphing the Equation
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Plot the Y-intercept: Start by plotting the point \( (0, 5) \) on the graph.
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Use the Slope: The slope \( -\frac{2}{3} \) indicates that for every 3 units you move to the right (positive direction on the x-axis), you move down 2 units (negative direction on the y-axis).
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Finding another point: From the y-intercept \( (0, 5) \):
- Move 3 units to the right: \( (0 + 3, 5) \Rightarrow (3, 5) \)
- Then, move down 2 units: \( (3, 5 - 2) \Rightarrow (3, 3) \)
Therefore, another point on the line is \( (3, 3) \).
- Draw the line: Connect the points \( (0, 5) \) and \( (3, 3) \) with a straight line, and extend the line in both directions.
This will give you the graph of the linear equation \( y = -\frac{2}{3}x + 5 \). If you were to visualize it, it would slope downwards from left to right.