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An equation of a straight line in a coordinate plane which has the slope m and passes through the given point P = (a,b) is
y - b = m*(x-a). (1)
Simply substitute the given data into equation (1), and you will get
y-2 = (-5/6)*(x-6). (2)
It is the equation in the "slope intercept form".
If you want to get the standard form equation, simplify (2):
6y-12 = -5x + 30, or, equivalently, 5x + 6y = 30 + 12,
or, finally, 5x+6y = 42.
Solved.
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- Equation for a straight line having a given slope and passing through a given point