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Find the slope of a line perpendicular to the line whose equation is x-2y=14​

User Mesutozer
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Final answer:

The slope of a line perpendicular to the line with the equation x - 2y = 14 is -2 because perpendicular slopes are negative reciprocals.

Step-by-step explanation:

To find the slope of a line perpendicular to another line, you must first know the slope of the original line.

The equation given is x - 2y = 14, which we can rewrite in slope-intercept form (y = mx + b) to find its slope.

By adding 2y to both sides and subtracting 14 from both sides, we get 2y = x - 14.

Then, we divide both sides by 2 to solve for y, resulting in y = 1/2x - 7. Thus, the slope (m) of this line is 1/2.

Perpendicular lines have slopes that are negative reciprocals of each other.

So, if the slope of the original line is 1/2, the slope of a line perpendicular to it would be the negative reciprocal of 1/2, which is -2 (flipping the fraction and changing the sign).

All lines that are perpendicular to the original line will have this slope of -2, regardless of their y-intercept.

User Saeid Doroudi
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