To find the y-intercept of the line passing through the points (2, 5) and (-2, -11), we first need to determine the equation of the line in slope-intercept form (y = mx + b).
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Calculate the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (2, 5) and (-2, -11): \[ m = \frac{-11 - 5}{-2 - 2} = \frac{-16}{-4} = 4 \]
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Use the point-slope form to find the line's equation: We can use one of the points and the slope to find the equation. Using point (2, 5): \[ y - 5 = 4(x - 2) \] Expanding this: \[ y - 5 = 4x - 8 \] \[ y = 4x - 3 \]
Now, we can read the y-intercept (b) directly from the equation \(y = 4x - 3\), which is \(-3\).
So, the y-intercept of the line is \(-3\).
Answer: -3
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