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.
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.
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