To determine the correct graph that represents the points (1,5), (2,7), (3,9), and (4,11), we first need to find the relationship between these points.
Let's analyze the points:
- (1, 5)
- (2, 7)
- (3, 9)
- (4, 11)
You can see that the y-values are increasing by 2 for each increase of 1 in the x-values:
- From (1,5) to (2,7): 5 + 2 = 7 (increase of 2)
- From (2,7) to (3,9): 7 + 2 = 9 (increase of 2)
- From (3,9) to (4,11): 9 + 2 = 11 (increase of 2)
This pattern suggests that the equation of the line can be expressed in the form of a linear function, specifically:
\[ y = 2x + 3 \]
Where:
- The slope (m) is 2 (this indicates the line rises 2 units for every 1 unit it moves horizontally).
- The y-intercept (b) is 3 (the point where the line crosses the y-axis).
Now, let’s visualize:
- At x = 1, y = 2(1) + 3 = 5 (correct)
- At x = 2, y = 2(2) + 3 = 7 (correct)
- At x = 3, y = 2(3) + 3 = 9 (correct)
- At x = 4, y = 2(4) + 3 = 11 (correct)
So, the correct graph would show a straight line passing through these four points:
- (1,5)
- (2,7)
- (3,9)
- (4,11)
Without the actual images, I cannot specify which graph corresponds to this equation. However, you should look for a straight line that passes through all the four indicated points.
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