Question 708148
What is important is to not let the fact that the coordinates for y being variables bother you.  


Slope intercept form: y=mx+B
Slope formula: {{{m=(y[1]-y[2])/(x[1]-x[2])}}}
Formula for y Intercept: B=y-mx
Change from convention ----- I'm using B for the y intercept because "b" is already taken by our problem for another purpose.


Do some calculations:
m=(b-a)/(7-2),
m=(b-a)/5
Pick one of the given points and use it to find B, the y-intercept.
Picking (2,a).
{{{B=a-(m)*2}}}
{{{B=a-(b-a)*2/5}}}
{{{B=a/5-2(b-a)/5}}}
{{{B=(a-2b+2a)/5}}}


Formula For Line: {{{y=((b-a)/5)x+(a-2b+2a)/5}}}