Final answer:
The equation of a line parallel to y = 9 + 3x that passes through (3, -2) is y = 3x - 11, and the equation of a line perpendicular to y = 9 + 3x that passes through (3, -2) is y = -1/3x + 1.
Step-by-step explanation:
The equation of a line that is parallel to the line y = 9 + 3x will have the same slope, which is 3.
To find the y-intercept of our parallel line, we use the point (3, -2) and the slope 3 in the point-slope form which is y - y1 = m(x - x1).
Substituting the given point and slope, we get y + 2 = 3(x - 3), which simplifies to y = 3x - 11.
To find the equation of a line perpendicular to y = 9 + 3x, we need a slope that is the negative reciprocal of 3, which is -1/3.
Using the point (3, -2) and the slope -1/3 in the point-slope formula, we get y + 2 = -1/3(x - 3), which simplifies to y = -1/3x + 1.