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Which equation represents a line which is parallel to the line 7y-x=-56 ? Answer y=-(1)/(7)x+7 y=(1)/(7)x-1 y=7x-4 y=-7x-2

Which equation represents a line which is parallel to the line 7y−x=−567y - x = -56 ?\newlineAnswer\newliney=−17x+7y = -\frac{1}{7}x + 7\newliney=17x−1y = \frac{1}{7}x - 1\newliney=7x−4y = 7x - 4\newliney=−7x−2y = -7x - 2

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Full solution

Q. Which equation represents a line which is parallel to the line 7y−x=−567y - x = -56 ?\newlineAnswer\newliney=−17x+7y = -\frac{1}{7}x + 7\newliney=17x−1y = \frac{1}{7}x - 1\newliney=7x−4y = 7x - 4\newliney=−7x−2y = -7x - 2
  1. Find Slope: First, find the slope of the given line 7y−x=−567y - x = -56. Rewrite in slope-intercept form (y=mx+b)(y = mx + b). 7y=x−567y = x - 56 y=17x−8y = \frac{1}{7}x - 8 Slope (m)=17(m) = \frac{1}{7}
  2. Identify Parallel Line: Parallel lines have the same slope. So, the slope of the parallel line is also 17 \frac{1}{7} .
  3. Check Options: Check the given options for the same slope. y=−17x+7 y = -\frac{1}{7}x + 7 (Slope = −17 -\frac{1}{7} , not parallel) y=17x−1 y = \frac{1}{7}x - 1 (Slope = 17 \frac{1}{7} , parallel) y=7x−4 y = 7x - 4 (Slope = 7 7 , not parallel) y=−7x−2 y = -7x - 2 (Slope = −7 -7 , not parallel)
  4. Final Equation: The equation y=17x−1y = \frac{1}{7}x - 1 has the same slope as the given line.

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