What is the y-intercept of the line that is parallel to 2x + 3y = 4 and contains the point (6, -2)?
the given equation is,
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To find the y-intercept of the line parallel to (2x + 3y = 4) and passing through the point ((6, -2)), first, find the slope of the given line. Then, use the point-slope form of the equation to find the y-intercept.
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Convert the given equation to slope-intercept form: (y = mx + b), where (m) is the slope and (b) is the y-intercept. [2x + 3y = 4] [3y = -2x + 4] [y = -\frac{2}{3}x + \frac{4}{3}]
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The slope of the given line is (-\frac{2}{3}).
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Since the line we're looking for is parallel, it will have the same slope.
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Use the point-slope form of the equation: (y - y_1 = m(x - x_1)), where ((x_1, y_1)) is the given point and (m) is the slope. [y - (-2) = -\frac{2}{3}(x - 6)] [y + 2 = -\frac{2}{3}(x - 6)]
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To find the y-intercept, let (x = 0) and solve for (y): [y + 2 = -\frac{2}{3}(0 - 6)] [y + 2 = -\frac{2}{3}(-6)] [y + 2 = 4] [y = 4 - 2] [y = 2]
Therefore, the y-intercept of the line parallel to (2x + 3y = 4) and passing through the point ((6, -2)) is (2).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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