To determine the equation of the linear function represented by the points \( (X, Y) = (-4, 11) \) and \( (-3, 12) \), we can first find the slope of the line. The slope \( m \) is calculated using the formula:
\[ m = \frac{Y_2 - Y_1}{X_2 - X_1} \]
Using the points \( (-4, 11) \) as \( (X_1, Y_1) \) and \( (-3, 12) \) as \( (X_2, Y_2) \):
\[ m = \frac{12 - 11}{-3 - (-4)} = \frac{1}{1} = 1 \]
The slope \( m \) is \( 1 \).
Next, we can use the point-slope form of the linear equation, which is:
\[ Y - Y_1 = m(X - X_1) \]
Using the point \( (-4, 11) \):
\[ Y - 11 = 1(X - (-4)) \]
This simplifies to:
\[ Y - 11 = X + 4 \]
Adding 11 to both sides:
\[ Y = X + 15 \]
Thus, the equation of the line is:
\[ Y = X + 15 \]
This is the best representation of the linear function based on the plotted points.
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