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Find the slope of a line perpendicular to the line whose equation is x, minus, 2, y, equals, 14x−2y=14. Fully simplify your answer.

Question

Find the slope of a line perpendicular to the line whose equation is x, minus, 2, y, equals, 14x−2y=14. Fully simplify your answer.

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Solution

The first step is to rewrite the equation in the slope-intercept form (y = mx + b), where m is the slope of the line. The given equation is x - 2y = 14.

Step 1: Subtract x from both sides to get -2y = 14 - x.

Step 2: Divide every term by -2 to solve for y. This gives us y = 1/2x - 7.

So, the slope of the given line is 1/2.

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line perpendicular to the given line is the negative reciprocal of 1/2, which is -2.

This problem has been solved

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