QuestionFind the slope of a line perpendicular and a line parallel to .
Studdy Solution
STEP 1
Assumptions1. The equation of the line is given by
. The slope of a line given by the equation is
3. The slope of a line perpendicular to a line with slope is
4. The slope of a line parallel to a line with slope is also
STEP 2
First, we identify the slope of the given line. The slope is the coefficient of in the equation of the line.
In the equation , the slope is .
STEP 3
To find the slope of a line perpendicular to the given line, we take the negative reciprocal of the slope of the given line.
If is the slope of the given line, then the slope of the line perpendicular to it, , is given by
STEP 4
Substitute for in the equation from3 to find the slope of the line perpendicular to the given line.
STEP 5
Calculate the slope of the line perpendicular to the given line.
STEP 6
To find the slope of a line parallel to the given line, we use the fact that parallel lines have the same slope.
So, the slope of a line parallel to the given line is the same as the slope of the given line, .
The slope of a line perpendicular to the given line is and the slope of a line parallel to the given line is .
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