$\"\"$

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The line equations are Line a: $\"\"$ , Line b: $\"\"$ , and Line c: $\"\"$ .

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Rewrite the equation of line a: $\"\"$ in the slope - intercept form by solving for y.

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Add 2x to each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore slope of line a is 2. $\"\"$

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Rewrite the equation of line b: $\"\"$ in the slope - intercept form by solving for y.

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Subtract 2x from each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Divide each side by 5.

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$\"\"$

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$\"\"$

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Therefore slope of line b is $\"\"$ . $\"\"$

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Rewrite the equation of line c: $\"\"$ in the slope - intercept form by solving for y.

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Subtract x from each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Divide each side by 2.

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$\"\"$

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$\"\"$

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Therefore slope of line c is $\"\"$ .

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Therefore slopes of line a, line b and line c are $\"\"$ respectively.

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The line a has a slope of 2, the negative reciprocal of $\"\"$ , so the lines a and c are perpendicular. $\"\"$

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The option D is correct answer.