SOLUTION: Line L has equation 2x - 3y = 5. Line M passes through the point (3, -10) and is parallel to line L. Determine the equation for line M.

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.    ANSWER  

    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.