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