Question 1145781
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Since the projected/requested line is parallel to the given line, its equation has the same co-named coefficients at x and y.


Hence, the projected/requested line has an equation of the form  2x - 3y = c with unknown coefficient "c".


To find "c", simply substitute the coordinates of the given point p and q as x and y respectively into this equation  2x - 3y = c.  

You will get


    2*3 - 3*(-10) = c,  


which implies  c = 6 + 30 = 36.


Thus your final equation of the projected/requested line in standard form is 


    2x - 3y = 36.    <U>ANSWER</U>  
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What you really need to know to solve such problems is <U>THIS</U>:


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    1.  Two parallel lines have the same slope.  It helps you when you are dealing with the slope-intersept form of equations.

        Therefore, the equations of parallel lines are identical in their "x-y" parts. The difference is only in their constant terms.


    2.  Two parallel lines have the same co-named coefficients in their standard form.

        Therefore, the equations of parallel lines are identical in their "x-y" parts. The difference is only in their constant terms.


    3.  To find the unknown constant term in the equation for the projected/requested parallel line, simply substitute the coordinates of the

        given point into this equation.
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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-parallel-to-a-given-line-and-passing-through-a-given-point.lesson>Equation for a straight line parallel to a given line and passing through a given point</A>

in this site.