Question 179121
p = 20  ,  x  =  42  
because p = mx + b
then  
       20 = m(42) + b  ----------(1)
p = 10  ,  x  =  52  
then
      10 = m(52) + b  -----------(2)
2 equation with 2 variables
you can do many ways to solve it.
First way of solution:
Equation minus equation in each side
In the left side 20-10 = 10
in the right sied  (m(42) + b)-(m(52) + b) = (-10)m
then   10  = (-10)m
        m   =  -1
at the equation(1) put (-1) instead of m
       20 = (-1)(42) + b
       20 = -42 + b
       20 + 42  = b
       b = 62

Then  answer in the form p = mx + b  is 
             p = (-1)x + 62

The Second way of solution:
p = 20  ,  x  =  42  
because p = mx + b
then  
       20 = m(42) + b  ----------(1)
     
p = 10  ,  x  =  52  
then
      10 = m(52) + b  -----------(2)

From equation(1) b = 20 - 42m put this (20-42m) instead of b in the equation(2)
      10 = m(52) + (20-42m)
      10 = 10m + 20
      -10 = 10m
       m = (-1) 
Put this (-1) instead of m in the equation(2)
      10 = (-52) + b
      10 + 52  = b
      b = 62


Then  answer in the form p = mx + b  is 
             p = (-1)x + 62   (The same as the first solution)