1. Line passing through (5,4) and perpendicular to y = 3x + 7 (point-slope form):
Identify slope of given line:
y = 3x + 7 m = 3
Find perpendicular slope:
m_perp = -1/3
Use point-slope form:
y - y1 = m(x - x1)
y - 4 = -1/3(x - 5)
Answer: y - 4 = -1/3(x - 5)
2. Line passing through (5,3) and parallel to y = -1/5x + 5 (slope-intercept form):
Identify slope of given line:
y = -1/5x + 5 m = -1/5
Use point-slope form:
y - 3 = -1/5(x - 5)
Convert to slope-intercept form:
y - 3 = -1/5x + 1
y = -1/5x + 4
Answer: y = -1/5x + 4