Question 795462
The given equation has three variables.  Your given point, F, will give values to the variables x and y, leaving only the variable c as unknown.  You would then just solve for c and simplify.  


A clear method which you can choose, is solve for c FIRST.  Substitute the values from F into the formula for c and evaluate.  



Performing that described method:
{{{y=(5/3)x+c}}}.   Point F on the line is given as (4,-6).
Solving for c,
{{{c=y-(5/3)x}}}
Substituting with point F,
{{{c=-6-(5/3)4}}}
{{{c=-6-20/3}}}
{{{c=(-18-20)/3}}}
{{{highlight(c=-38/3=-12&2/3)}}}


The equation in the two variables x and y, is {{{highlight(y=(5/3)x-12&2/3)}}}


Drawing the graph is just a matter of indicating the y-intercept, which is c in your equation, and using the slope, {{{5/3}}}.
Note, knowing the given point F, you can also graph the line by indicating (4,-6) on the cartesian plane and using the slope, {{{5/3}}}.  In this way, if you make your axes suitably, you can read the y-intercept directly from the graphed line.