SOLUTION: How do you write an equation of the line containing the given point and parallel to the given line? (5,-9); 6x-5y=7

In order for the line under the question be parallel to the given line  6x - 5y = 7,

the left side of its equation must be exactly the same  6x - 5y = something.


For now, I will write this equation in the form


    6x - 5y = c,    (*)


where "c" is the constant term, now unknown to us.



To find its value, use the condition that the line contains the point (5,-9).



It means that the equation (*) must be satisfied when the values of the point coordinate  x= 5  and  y= -9  are substituted 

into the equation.  It gives


   6*5 - 5*(-9) = c = 30 + 45 = 75.


So, you found the value of "c" :  c = 75,  and now your equation (*)  becomes


    6x - 5y = 75.