To determine which graph depicts the correct relationship for the points (1,5), (2,7), (3,9), and (4,11), let's first identify any patterns.
The points can be outlined as follows:
- (1, 5)
- (2, 7)
- (3, 9)
- (4, 11)
We can observe that as \( x \) increases by 1, \( y \) increases by 2. This indicates a linear relationship.
To extract the formula, we can identify the slope (\( m \)):
\[ m = \frac{change : in : y}{change : in : x} = \frac{7 - 5}{2 - 1} = 2 \]
Now, we can find the y-intercept (\( b \)), which can be determined using one of the points. Substituting \( x = 1 \) and \( y = 5 \) into the slope-intercept form \( y = mx + b \):
\[ 5 = 2(1) + b \implies b = 5 - 2 = 3 \]
Thus, the equation that represents this relationship is:
\[ y = 2x + 3 \]
Now, you need to choose the graph that represents this line. Look for a line that passes through the points (1,5), (2,7), (3,9), and (4,11) consistently, showing the given linear equation \( y = 2x + 3 \).
If you have the graphs available, select the one that meets this criterion.
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