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Write the standard form equation of the line that passes through the point p and is perpendicular to the line l.
p : (-3, -3)
l : y = 1/2 x + 3
Write the standard form equation of the line that passes through the point p and is parallel to the line l.
p : (-1, 0)
l : y = 8/3 x – 17/3
To find the standard form equation of the lines based on the given points and lines, follow these steps:
### Part 1: Line Perpendicular to Line l
1. Identify the slope of line l:
The slope from the equation ( l: y = frac{1}{2}x + 3 ) is ( frac{1}{2} ).
2. Find the slope of the perpendicular line:
The slope of a line that is perpendicular to another is the negative reciprocal. Thus, the perpendicular slope ( m ) is:
[
m = -frac{1}{left(frac{1}{2}right)} = -2
]
3. Use point-slope form with point p (-3, -3):
The equation is:
[
y – y_1 = m(x – x_1)
]
Substituting the point and slope:
[
y + 3 = -2(x + 3)
]
4. Rearranging to standard form (Ax + By = C):
[
y + 3 = -2x – 6 \
2x + y + 9 = 0
]
Thus, the standard form is:
[
2x + y = -9
]
### Part 2