Question

1. through: (3, -1), perp. to y = x + 4

Explanation:

Step1: Find slope of perpendicular line

The given line is \( y = x + 4 \), its slope \( m_1 = 1 \). For perpendicular lines, \( m_1 \times m_2=-1 \), so \( m_2=-1 \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(3,-1) \) and \( m=-1 \).
Substitute values: \( y - (-1)=-1(x - 3) \)
Simplify: \( y + 1=-x + 3 \)
Then \( y=-x + 2 \)

Answer:

The equation of the line is \( y=-x + 2 \)