To find the correct formula for the points (1,5), (2,7), (3,9), and (4,11), we can first identify a pattern or relationship among these points.
Let's examine the y-values relative to the x-values:
- For x = 1, y = 5
- For x = 2, y = 7
- For x = 3, y = 9
- For x = 4, y = 11
We can observe that as x increases by 1, y increases by 2. This suggests a linear relationship of the form:
\[ y = mx + b \]
where \( m \) is the slope, and \( b \) is the y-intercept.
Calculating the slope (m):
\[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{(7 - 5)}{(2 - 1)} = \frac{2}{1} = 2 \]
Now, we can use one of the points to find the value of \( b \). Let's use the point (1, 5):
\[ 5 = 2(1) + b \]
Solving for b gives us:
\[ 5 = 2 + b \implies b = 3 \]
Thus, the linear equation that represents these points is:
\[ y = 2x + 3 \]
Now, to depict this graphically:
- The intercept should be at (0, 3) on the y-axis.
- The slope of the line should rise 2 units for every 1 unit it moves to the right.
When plotted, the line should go through the points (1, 5), (2, 7), (3, 9), and (4, 11) as described.
If you have options for graphs, look for a line that passes through these points and has the equation \( y = 2x + 3 \).
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