To determine which graph accurately depicts the points (1, 5), (2, 7), (3, 9), and (4, 11), we should first identify the relationship between the points.
Looking at the points:
- (1, 5)
- (2, 7)
- (3, 9)
- (4, 11)
We can see that the y-values increase by 2 for each 1-unit increase in the x-values. This indicates a linear relationship.
We can describe this linear relationship with the formula for a straight line in the form \( y = mx + b \).
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The slope (m) can be calculated as \( \frac{\Delta y}{\Delta x} \):
- Between points (1,5) and (2,7), the slope \( m = \frac{7 - 5}{2 - 1} = 2 \).
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Now, we use one point to find the y-intercept (b). Using point (1, 5):
- Substitute into the equation: \( 5 = 2(1) + b \)
- This results in \( 5 = 2 + b \), therefore, \( b = 3 \).
So the correct linear equation that represents these points is: \[ y = 2x + 3 \]
To accurately determine which graph depicts this equation, you would look for a line with a slope of 2 that intersects the y-axis at 3, passing through all the specified points.
Since the options provided include images that cannot be analyzed in this text format, you would need to visually inspect the graphs based on the determined equation to find the one that matches.
Look for the following:
- A line that clearly goes through all the points (1, 5), (2, 7), (3, 9), and (4, 11).
- The line should have a steepness corresponding to a slope of 2.
Make your choice based on which graph matches these criteria.
1 answer