Question 217241
x-2y=4
2x-4y=-12


Step 1.  Let's put the above equations in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).  


Step 2.  Let's start with {{{x-2y=4}}}


Add 2y-4 to both sides of the equation


{{{x-2y+2y-4=4+2y-4}}}


{{{x-4=2y}}}


Divide 2 to both sides of the equation


{{{x/2-4/2=2y/2}}}


{{{x/2-2=y}}} or {{{y=x/2-2}}}


Step 3.   In Step 2, the slope m=1/2 and the y-intercept b=-2.


Step 4.  Next, let's look at {{{2x-4y=-12}}} and put it in slope-intercept form.


Add 4y+12 to both sides of the equation


{{{2x-4y+4y+12=-12+4y+12}}}


{{{2x+12=4y}}}


Divide 4 to both sides of the equation.


{{{2x/4+12/4=4y/4}}}


{{{x/2+3=y}}} or {{{y=x/2+3}}}


Step 4.   In Step 3, the slope m=1/2 and the y-intercept b=3.


Step 5.  ANSWER:  Based on Steps 2 and 4, the slopes are both equal to 1/2 which means the lines are parallel. This will be evident on the graph below in Step 6.


{{{y=x/2-2}}}

{{{y=x/2+3}}}


Step 6.  ANSWER:  Now, graph the equations that is now in slope-intercept form (note on the graph the y-intercepts at x=0 to know which equation is which)


{{{graph(400,400,-10, 10, -10, 10, x/2-2,x/2+3)}}}


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J