The line equation in slope-intercept form is , where m is the slope and b is the y-intercept.

If two lines are perpendicular, the slope (m₁) of one line is opposite reciprocal of the second line slope (m₂). It can be represented as, .

The slope of the lineis .

So the line perpendicular to above equation has the slope .  

Substitute (x₁, y₁) = ( -3,1) and in the point-slope form equation 

                   (Substitute (x₁, y₁) and m values)

                         (Product of two same signs is positive)

                    (Apply distributive property: a(b + c) = ab + ac))

                                (Cancel common terms)                            

             (Add 1 to each side)                                 

                         (Additive inverse property: )

                         (Additive identity property: )

                                 (Add: )                     

The required slope-intercept form of the line equation is