Find the slope of a line perpendicular to the line whose equation is x, plus, y, equals, minus, 6x+y=−6. Fully simplify your answer.
Question
Find the slope of a line perpendicular to the line whose equation is x, plus, y, equals, minus, 6x+y=−6. Fully simplify your answer.
Solution
The given equation is x + y = -6.
First, we need to find the slope of the given line. To do this, we rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.
Subtract x from both sides of the equation to get y = -x - 6.
So, the slope of the given line is -1.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
The negative reciprocal of -1 is 1.
So, the slope of the line perpendicular to the given line is 1.
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