SOLUTION: Find the equation of the line through (2,a) and (7,b).

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Question 708148: Find the equation of the line through (2,a) and (7,b).
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29
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-%28m%29%2A2
B=a-%28b-a%29%2A2%2F5
B=a%2F5-2%28b-a%29%2F5
B=%28a-2b%2B2a%29%2F5

Formula For Line: y=%28%28b-a%29%2F5%29x%2B%28a-2b%2B2a%29%2F5