Question 174289
Your two points in ({{{x}}},{{{p}}}) form are ({{{x[1]}}},{{{p[1]}}}) = (42,20) and ({{{x[2]}}},{{{p[2]}}}) = (52,10).


The two-point form of the equation of a line is {{{y-y[1]=((y[2]-y[1])/(x[2]-x[1]))(x-x[1])}}}, except in this case you would substitute {{{p}}} for {{{y}}}.


Substitute the coordinate values into {{{p-p[1]=((p[2]-p[1])/(x[2]-x[1]))(x-x[1])}}}.  Then do the indicated arithmetic and finally solve the equation for {{{p}}} to end up with your equation in slope-intercept ({{{p=mx+b}}}) form.