SOLUTION: i need to graph these equations but i dont know how x+2y=6 3x-y=4 y=1/2x-3 y-2=-2(x-3)

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Question 278209: i need to graph these equations but i dont know how
x+2y=6
3x-y=4
y=1/2x-3
y-2=-2(x-3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to show you how to do these.


First, we must solve for 'y' (if not already solved for y).


x%2B2y=6 Start with the given equation.


2y=6-x Subtract x from both sides.


2y=-x%2B6 Rearrange the terms.


y=%28-x%2B6%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-1%29%2F%282%29%29x%2B%286%29%2F%282%29 Break up the fraction.


y=-%281%2F2%29x%2B3 Reduce.


Looking at y=-%281%2F2%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1%2F2 and the y-intercept is b=3


Since b=3 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -1%2F2, this means:

rise%2Frun=-1%2F2


which shows us that the rise is -1 and the run is 2. This means that to go from point to point, we can go down 1 and over 2



So starting at , go down 1 unit


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=-%281%2F2%29x%2B3

So this is the graph of y=-%281%2F2%29x%2B3 through the points and