To find the equation of the line that passes through the points \((6, -6)\) and \((8, 8)\), we can follow these steps:
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Find the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (6, -6)\) and \((x_2, y_2) = (8, 8)\).
Calculate the slope: \[ m = \frac{8 - (-6)}{8 - 6} = \frac{8 + 6}{2} = \frac{14}{2} = 7 \]
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Use the point-slope form of a line equation, which is: \[ y - y_1 = m(x - x_1) \] We can use either of the points. Let's use point \((6, -6)\):
Substitute \(m = 7\), \(x_1 = 6\), and \(y_1 = -6\) into the formula: \[ y - (-6) = 7(x - 6) \] This simplifies to: \[ y + 6 = 7(x - 6) \]
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Distribute and simplify: \[ y + 6 = 7x - 42 \] Now, isolate \(y\) by subtracting 6 from both sides: \[ y = 7x - 42 - 6 \] \[ y = 7x - 48 \]
Thus, the equation of the line in slope-intercept form is: \[ y = 7x - 48 \]