1. The problem is to find the equation of a line with a given gradient (slope) of $-2$. 2. The general formula for the equation of a line in slope-intercept form is: $$y = mx + c$$ where $m$ is the gradient and $c$ is the y-intercept. 3. Since only the gradient $m = -2$ is given, the equation of the line can be written as: $$y = -2x + c$$ 4. Without additional information such as a point on the line, the value of $c$ (the y-intercept) cannot be determined. 5. Therefore, the equation of the line with gradient $-2$ is: $$y = -2x + c$$ where $c$ is any real number representing the y-intercept. This represents all lines with slope $-2$.