SOLUTION: Graph the equation 3y-6=-9x by makin an input-output table

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Question 116668: Graph the equation 3y-6=-9x by makin an input-output table
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3y-6=-9x……solve for y
3y=-9x+%2B+6……divide both sides by 3
y=-3x+%2B+2……
make an input-output table:
let x be -2,-1,0, 1, 2
calculate y for these values:
y=-3x+%2B+2……for x=-2
y=-3%28-2%29+%2B+2=+6%2B2=8……
y=-3x+%2B+2……for x=-1
y=-3%28-1%29+%2B+2=+3%2B2=5……

y=-3x+%2B+2……for x+=+0
y=-3%280%29+%2B+2=+0%2B2=5……
y=-3x+%2B+2……for x+=+1
y=-3%281%29+%2B+2=+-3%2B2=+-1……
y=-3x+%2B+2……for x+=+2
y=-3%282%29+%2B+2=+-6%2B2=+-4……


x | y
-2| 8
-1| 5
0 | 2
1 | -1
2 | -4
Now you can graph it.
Here is the graph:



Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-3%2Ax%2B2 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-2

y=-3%2A%28-2%29%2B2

y=6%2B2 Multiply

y=8 Add

So here's one point (-2,8)




Now lets find another point

Plug in x=-1

y=-3%2A%28-1%29%2B2

y=3%2B2 Multiply

y=5 Add

So here's another point (-1,5). Add this to our graph





Now draw a line through these points

So this is the graph of y=-3%2Ax%2B2 through the points (-2,8) and (-1,5)


So from the graph we can see that the slope is -3%2F1 (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 1 units to get to the next point), the y-intercept is (0,2)and the x-intercept is (0.666666666666667,0) ,or (2%2F3,0)


We could graph this equation another way. Since b=2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,2).


So we have one point (0,2)





Now since the slope is -3%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,2), we can go down 3 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=-3%2Ax%2B2


So this is the graph of y=-3%2Ax%2B2 through the points (0,2) and (1,-1)