To analyze the line passing through the points \((-2, 0)\) and \((2, -4)\), we can determine its slope, equation, and intercepts.
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Calculate the slope (m): The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (-2, 0)\) and \((x_2, y_2) = (2, -4)\): \[ m = \frac{-4 - (0)}{2 - (-2)} = \frac{-4}{4} = -1 \]
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Equation of the line: We can use point-slope form \(y - y_1 = m(x - x_1)\) with the point \((-2, 0)\): \[ y - 0 = -1(x - (-2)) \ y = -x - 2 \]
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Y-intercept: To find the y-intercept, set \(x = 0\) in the line equation: \[ y = -0 - 2 = -2 \] Therefore, the y-intercept is \((0, -2)\).
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X-intercept: To find the x-intercept, set \(y = 0\) in the line equation: \[ 0 = -x - 2 \ x = -2 \] Therefore, the x-intercept is \((-2, 0)\), which is one of our given points.
Now let's summarize true statements about the line:
- The slope of the line is \(-1\).
- The line crosses the y-axis at \((0, -2)\).
- The line has an x-intercept at \((-2, 0)\).
From the computations and corresponding interpretations of these characteristics, any statements validating these points can be marked as true. If you have specific statements, please share them, and I can confirm which are true based on the calculations.