9514 1404 393
Answer:
- parallel: y = -7x -44
- perpendicular: y = 1/7x -8/7
Step-by-step explanation:
The given equation is in slope-intercept form:
y = mx +b . . . . . . line with slope m and y-intercept b
For the purpose of this question, you need to recognize that the line with equation ...
y = -7x +8
has a slope (x-coefficient) of -7.
The parallel line will have the same slope (x-coefficient).
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/(-7) = 1/7
Each line will have a y-intercept (b) that makes the line go through the given point. The y-intercept can be found by solving the slope-intercept equation for b:
b = y - mx . . . . . . where (x, y) is the point you want the line to go through
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parallel line:
b = -2 -(-7)(-6) = -2 -42 = -44
The equation of the parallel line is y = -7x -44.
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perpendicular line:
b = -2 -(1/7)(-6) = -14/7 +6/7 = -8/7
The equation of the perpendicular line is y = 1/7x -8/7.
