To determine the equation of the linear function represented by the given points \( Y: 11, 12 \) and \( X: -4, -3 \), we need to first find the slope of the line based on these points. The two points can be represented as the coordinates \( (-4, 11) \) and \( (-3, 12) \).
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Calculate the slope (m) between the two points: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 11}{-3 - (-4)} = \frac{1}{1} = 1 \]
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Use the point-slope form of the equation of a line: The point-slope form is given as: \[ y - y_1 = m(x - x_1) \] We can use one of the points; let's choose \( (-4, 11) \): \[ y - 11 = 1(x + 4) \]
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Simplify the equation: \[ y - 11 = x + 4 \] \[ y = x + 15 \]
Thus, the equation of the linear function best represented by the graph is: \[ y = x + 15 \]
This is the equation of the line based on the two given points.
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