To determine which graph accurately depicts the formula for the points (1, 5), (2, 7), (3, 9), and (4, 11), we first need to identify a pattern in the coordinates.
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Identify the relationship between the x and y values:
- For (1, 5): \( y = 5 \)
- For (2, 7): \( y = 7 \)
- For (3, 9): \( y = 9 \)
- For (4, 11): \( y = 11 \)
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Find the pattern:
- The change in y-values as x increases is consistent:
- From 5 to 7 (increase of 2)
- From 7 to 9 (increase of 2)
- From 9 to 11 (increase of 2)
- The change in y-values as x increases is consistent:
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Formulate the linear equation:
- The points suggest a linear relationship. The y-intercept can be calculated: when \( x = 0 \), \( y \)would be expected to be 3 (since when \( x = 1\), \( y = 5 \); and thus follows the equation).
- Using the slope-intercept formula \( y = mx + b \), where \( m \) is the slope and \( b \) the y-intercept:
- The slope \( m = 2 \) and y-intercept \( b = 3 \).
- Thus, the equation is \( y = 2x + 3 \).
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Choose the appropriate graph:
- Look for a graph that represents the line described by the equation \( y = 2x + 3 \), which should pass through each of the given points.
If you can see the graphs in question, select the one that matches this linear formula. The graph will be a straight line starting from the y-axis at 3 and sloping up with a rise of 2 for every increase of 1 in x.
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