4. Determine the equation of the straight line passing through the point \( (3 ; 1) \) and with an angle of \( 135^{\circ} \).

To find the equation of the line, we first determine the slope. An angle of \( 135^{\circ} \) gives a slope calculated using the tangent function: \( m = \tan(135^{\circ}) = -1 \). Using the point-slope form of the equation \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) = (3, 1) \), we have: \[ y - 1 = -1(x - 3) \] Thus, simplifying gives us the equation of the line: \[ y = -x + 4. \] To visualize it better, this line has a negative slope, indicating it falls as you move from left to right. Therefore, at \( x = 0 \), the line intersects the y-axis at \( (0, 4) \). You can even plot values of \( x \) around \( 3 \) to see how \( y \) behaves; the line will cross through your chosen point and yield a clear downward slope, typical for slopes less than zero.