Question 53609
YOU'VE ASKED FOR A COMPLETE GEOMETRY LESSON USING GRAPHS. NOT WHAT WE'RE HERE FOR. BUT HERE'S SOME HELP.

THE EQUATION 4X-6Y=12 IN SLOPE INTERCEPT FORM IS -6Y=-4X+12 MULTIPLYING BOTH SIDES BY -I WE GET 6Y=4X-12 OR Y=4/6X-12/6 OR Y=2/3X-2 

NOW WE HAVE A LINE DEFINED BY A SLOPE OR 2/3 AND A Y INTERCEPT OF -2 (0,-2) WHICH SAYS WHEN THE X VALUE IS 0 THE Y VALUE IS -2.

SETTING THE Y VALUE TO ZERO WE FIND THE X INTERCEPR THUS 0=2/3X-2 OR 2/3X=2 OR CROSS MULTIPLYING WE GET 2X=6 OR X=6/2 OR X=3 WHEN Y=0 OR (3,0) IS A SECOND POINT ON THE LINE Y=2/3X-2.

TO FIND ANY OTHER POINT ON THIS LINE JUST IDENTIFY AN X OR A Y POINT SUBSTITUTE THIS VALUE IN THIS EQUATION Y=2/3X-2 AND SOLVE FOR THE OTHER UNKNOWN.