To match the equations with the lines shown on the graph, you would need to analyze the slopes and intercepts of each equation.
Here’s a breakdown of the given equations:
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y = 2/3x: This line has a positive slope of 2/3 and passes through the origin (0,0).
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y = 3/2x: This line has a positive slope of 3/2 and also passes through the origin (0,0), but it is steeper than the first equation.
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y = -3/2x - 4: This line has a negative slope of -3/2 and a y-intercept of -4, meaning it crosses the y-axis at (0, -4).
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y = 2x - 4: This line has a positive slope of 2 and a y-intercept of -4, meaning it crosses the y-axis at (0, -4), but is less steep than the previous negative slope line.
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y = 3x - 4: This line has a positive slope of 3 and a y-intercept of -4, making it the steepest of the positive slopes in the list.
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y = -1/2x: This line has a negative slope of -1/2 and passes through the origin (0,0).
To accurately match these equations to the lines in the graph, examine the following characteristics:
- Slope: Determine whether the line is increasing (positive slope) or decreasing (negative slope).
- Y-Intercept: See where the line crosses the y-axis.
You would be able to match the equations to the lines visually based on the characteristics above. Without seeing the graph, I cannot give you the exact matches, but you can use the details provided to make your selections!