To determine which graph accurately depicts the points (1,5), (2,7), (3,9), and (4,11), we first need to identify the relationship between the points.
Looking at the points:
- (1,5)
- (2,7)
- (3,9)
- (4,11)
We can observe the following:
- From (1,5) to (2,7), the y-value increases by 2 for an increase in x-value of 1.
- This pattern continues for (2,7) to (3,9) and from (3,9) to (4,11).
The points form a linear relationship with a consistent slope. We can express the relationship in the form of a linear equation \( y = mx + b \).
To find the slope (m):
- The slope is the change in y divided by the change in x.
- Slope (m) = (7-5)/(2-1) = 2, or in general, m = 2.
To find b (the y-intercept), we can use one of the points. Using the point (1,5):
- Plugging this into the equation \( y = mx + b \):
- \( 5 = 2(1) + b \)
- This gives \( b = 5 - 2 = 3 \).
Now we can write the function: \[ y = 2x + 3 \]
Next, we check which graph presents a line that passes through the points we calculated using the established formula \( y = 2x + 3 \).
If you can provide descriptions of the graphs presented, I can help determine which one fits this formula correctly. Otherwise, you can look for a straight line that passes through all four points on the coordinate plane to identify the correct one.