To determine the equation of the line that passes through the points (-3, 5) and (-4, -3), 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, let \((x_1, y_1) = (-3, 5)\) and \((x_2, y_2) = (-4, -3)\).
Plugging in the values: \[ m = \frac{-3 - 5}{-4 - (-3)} = \frac{-8}{-1} = 8 \]
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Use the point-slope form of the line's equation, which is: \[ y - y_1 = m(x - x_1) \] We can use one of the points (let’s use (-3, 5)).
Substituting \(m = 8\), \(x_1 = -3\), and \(y_1 = 5\): \[ y - 5 = 8(x + 3) \]
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Simplify to find the standard form of the equation: \[ y - 5 = 8x + 24 \] \[ y = 8x + 29 \]
Thus, the equation of the line that passes through the points (-3, 5) and (-4, -3) is: \[ y = 8x + 29 \]