QuestionConsider the line with the equation: Give the equation of the line parallel to Line 1 which passes through : Give the equation of the line perpendicular to Line 1 which passes through :
Studdy Solution
STEP 1
1. The given line has the equation .
2. A parallel line will have the same slope as the given line.
3. A perpendicular line will have a slope that is the negative reciprocal of the given line's slope.
4. Both lines must pass through the point .
STEP 2
1. Determine the slope of the given line.
2. Find the equation of the line parallel to the given line.
3. Find the equation of the line perpendicular to the given line.
STEP 3
Determine the slope of the given line:
The equation of the line is , which is in the slope-intercept form .
The slope of the line is .
STEP 4
Find the equation of the line parallel to the given line:
A parallel line will have the same slope, .
Use the point-slope form of the equation of a line, , where .
Substitute the values:
Simplify the equation:
The equation of the parallel line is:
STEP 5
Find the equation of the line perpendicular to the given line:
The slope of the perpendicular line is the negative reciprocal of , which is .
Use the point-slope form of the equation of a line, , where .
Substitute the values:
Simplify the equation:
The equation of the perpendicular line is:
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