How would you work out the equation of the normal at a point (2,5) given the equation of a line?

You are given the equation of a line in the form of y=mx+c. From this, you know that 'm' represents the gradient, which can also be represented as dy/dx. We now need to work out the gradient of the normal line. Using the equation M₁ multiplied by M₂ = -1, if M₁ = 2, then M₂ = -1/2. Now we have the gradient of the normal line, and as we are given the coordinates of the point of intersection, we can now use the equation y-y₁=m(x-x₁) where y₁ represents the y-coordinate and x₁ represents the x-coordinate to deduce the equation of the normal. If asked, we can also put it in the form y=mx+c.