by **HallsofIvy** » Tue Jul 21, 2020 5:25 pm

As said above, any (non-vertical) line in an xy-coordinate system can be written as y= ax+ b for some numbers a and b.

The graph goes through (2,30) so y= 30 when x= 2 so 30= 2a+ b and through (24,50) so y= 50 when x= 24 so 50= 24a+ b. Solve the equations 2a+ b= 30 and 24a+ b= 50 for a and b.

Since in both equations, b has coefficient 1, we can eliminate it by subtracting one equation from the other:

22a= 20 so a= 20/22= 10/11. (That is exactly the calculation for "slope" Baltuilhe gives).

Since a= 10/11, 2a+ b= 20/11+ b= 30, b= 30- 20/11= (330- 20)/11= 310/11.

The line is given by y= (10/11)x+ 310/11. That could also be written as 11y= 10x+ 310 or 11y- 10x= 310.