Which of the following is an equation of the line in the xy-plane that passes through the point (-(1)/(2),2) and is parallel to the line with equation y=-8x+3 ? Choose 1 answer: (A) y=(1)/(8)x+4 (B) y=(1)/(8)x+1 (c) y=-8x-2 (D) y=-8x+2

Question

Which of the following is an equation of the line in the  xy-plane that passes through the point  (-(1)/(2),2) and is parallel to the line with equation  y=-8x+3 ? Choose 1 answer: (A)  y=(1)/(8)x+4 (B)  y=(1)/(8)x+1 (c)  y=-8x-2 (D)  y=-8x+2

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Identify slope of line: Identify the slope of the given line. The equation of the given line is y = -8x + 3. This is in slope-intercept form (y = mx + b), where m is the slope. The slope of the given line is -8.Determine parallel line slope: Determine the slope of the line that is parallel to the given line. Lines that are parallel have the same slope. Therefore, the slope of the line we are looking for is also -8.Use point-slope form: Use the point-slope form to find the equation of the line. The point-slope form of a line is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We have the point (-(1)/(2), 2) and the slope -8. Plugging these into the point-slope form gives us (y - 2) = -8(x - (-1/2)).Simplify equation: Simplify the equation. First, distribute the -8: y - 2 = -8x - 8(-1/2). Simplify the right side: y - 2 = -8x + 4. Now, add 2 to both sides to get y by itself: y = -8x + 4 + 2. Finally, combine like terms: y = -8x + 6.Match equation to answer choices: Match the equation to the given answer choices. The equation we found is y = -8x + 6. This does not match any of the answer choices, indicating a potential error.

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