Question 1093523
Find the slope:    

(-1,1) - stays the same
(-4,-7) - change the signs. -subtracting x values and y values

-5 , -6  add the numbers vertically.      m(slope)= rise / run = -6/-5 = 6/5



Choose a point from the original problem. (4,7).    x=4       y=7   and    m= 6/5


Substitute all three values into the equation:  y=mx+b.  Then solve for b.
            
 y =  m    x  +  b
 7 =(6/5)(4) +  b     multiply the 6 and 4
 7 = 24/5  +    b      you get 24. Now multiply everything by 5.
 35 = 24  +  b           The fraction canceled.
 11  =  b                   Subtract 24 on both sides

Last Step:      Substitute  b = 11   and   m =  6/5   back into the equation :  y = m x  +  b

 y  =  6/5 x  +  11

Yay!!!   We now know that the points (-1,1) and (4,7) pass through the line y = 6/5 x + 11.