The equation \( y = -3x + 1 \) is a linear equation in slope-intercept form, where \( m = -3 \) is the slope and \( b = 1 \) is the y-intercept.
A linear equation like this typically represents a straight line on the Cartesian plane. As long as the equation is not degenerate (e.g., parallel to the x-axis or vertical line, which would have a different form), it will have infinitely many solutions. Each point \( (x, y) \) on the line is a solution to the equation.
Therefore, the equation \( y = -3x + 1 \) has infinitely many solutions.