Question 408100
 if a point (-2/3,5) is solution to {{{-3x+2y=-4}}} must lie on the line

so, generally speaking, the {{{condition}}} for a point (a, b) to lie on the line {{{y = mx + c}}} is: 

               {{{b = ma + c}}}

To determine whether a point lie on the line you have to just check whether the coordinates of the point given {{{satisfy}}} the equation or {{{not}}}. For this what you have to do is : Put the value of the {{{x}}} any {{{y}}} coordinates of the point and check whether it satisfy the equation {{{-3x+2y=-4}}} or not. 


{{{-3x+2y=-4}}}........plug in {{{x=-2/3}}} and {{{y=5}}}...if you get left side of equation equal to {{{-4}}}, then (-2/3,5) is solution to {{{-3x+2y=-4}}}


{{{-3(-2/3)+2*5=-4}}}

{{{-cross(3)(-2/cross(3))+10=-4}}}

{{{-(-2)+10=-4}}}

{{{2+10=-4}}}

{{{12=-4}}}...........it's not a solution

check:

{{{-3x+2y=-4}}}..... write it slope-intercept form

{{{y=-(3/2)x-2}}}...let see if point lie on a line



{{{ graph( 300, 200, -6, 5, -10, 10,  -(3/2)x-2) }}}


now you can plot a point (-2/3,5) and see it does not lie on that line