Question 218071
Graph the equation and show your slope: -4x-2y=-6


Step 1.  Let's put the equation 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.  Putting {{{-4x-2y=-6}}} in slope-intercept form yields the following steps.


Add 2y+6 to both sides of the equation


{{{-4x-2y+2y+6=-6+2y+6}}}


{{{-4x+6=2y}}}


Divide 2y to both sides of the equation


{{{-4x/2+6/2=2y/2}}}


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


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


Step 3.  ANSWER:  The equation is {{{y=-2x+3}}} where the slope m=-2 and y-intercept b=3.


Need one more point to graph the line since we have (0,3) as one point.  A slope m=-2 means every move to one unit to the right yields two step downward.


So starting at (0,3) then one unit to the right means x2=0+1=1 and then two units down means y2=3-2=1.  Then, the other point we can use to plot the line is (1,1).  We can check if it satisfies the equation  {{{y=-2x+3}}} or


{{{1=-2*1+3}}} which it does.


Here's the graph:


{{{graph(400,400,-5, 5, -5, 5, -2x+3)}}}



I hope the above steps and explanation were helpful. 


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Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J


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