Question 880335
The line containing (4,-2) and parallel to -5x+6y=-2 will have the same slope but a different constant.


Assuming you do not understand Standard Form, convert the given equation into slope-intercept form:
{{{6y=5x+(-2)}}}
{{{y=(5/6)x-2/6}}}
{{{y=(5/6)x-1/3}}}
... and the slope you want is {{{highlight_green(highlight_green(5/6))}}}.


Let us put that back into the equation we want to find, and change back from slope-intercept form to standard form.
{{{y=(5/6)x+b}}}, because at this point we do not know the y-intercept
{{{y-(5/6)x=b}}}
{{{-(5/6)x+y=b}}}
{{{-5x+6y=6b}}},
This is back into standard form, but we want to know what is the value of 6b.


Substitute the point which is supposed to be contained on this line, the given point (4,-2) and compute 6b.  You do not need to solve for b here; you only want the value of 6b as the combined constant.  
{{{-5(4)+6(-2)=6b}}}
{{{-20-12=6b}}}
{{{highlight_green(6b=-32)}}}
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The use of "b" is for the y-intercept in the slope-intercept equation form.  In this specific problem example, we need 6b for the standard form equation.
Finally our wanted equation is {{{highlight(-5x+6y=-32)}}}.