To find the equation of the linear function represented by the points \((-4, 3)\) and \((4, 11)\), we can use the slope-intercept form of a linear equation, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
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Calculate the slope (m): The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((-4, 3)\) (let's call this \((x_1, y_1)\)) and \((4, 11)\) (let's call this \((x_2, y_2)\)): \[ m = \frac{11 - 3}{4 - (-4)} = \frac{8}{4 + 4} = \frac{8}{8} = 1 \]
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Find the y-intercept (b): We can use one of the points to solve for \(b\). Using the point \((4, 11)\): \[ y = mx + b \] Substituting the values: \[ 11 = 1(4) + b \ 11 = 4 + b \ b = 11 - 4 \ b = 7 \]
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Write the equation: Now that we have \(m = 1\) and \(b = 7\), we can write the equation of the line: \[ y = 1x + 7 \ y = x + 7 \]
Thus, the equation best represented by the graph given the points is: \[ y = x + 7 \]