SOLUTION: How do I determine 'a' and 'b' such that the line with equation ax+by=4 passes through the point (5, 2) and has a slope of 2/3.

Algebra ->  Linear-equations -> SOLUTION: How do I determine 'a' and 'b' such that the line with equation ax+by=4 passes through the point (5, 2) and has a slope of 2/3.      Log On


   

Question 793744: How do I determine 'a' and 'b' such that the line with equation ax+by=4 passes through the point (5, 2) and has a slope of 2/3.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the line passes through the point (5, 2),
a%2A5%2Bb%2A2=4 or 5a%2B2b=4
Solving for y,
ax%2Bby=4-->by=-ax%2B4-->y=%28-a%2Fb%29x%2B4%2Fb
we get the equation in the slope intercept form, where the slope is the coefficient of x, so
-a%2Fb=2%2F3-->-3a=2b

Now we solve the system
system%285a%2B2b=4%2C-3a=2b%29-->5a-3a=4-->2a=4-->a=2
and substituting into -3a=2b we get
-3%2A2=2b-->b=-3