SOLUTION: Graph 3x + 2y = 6. Requires a graph!

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Question 110803: Graph 3x + 2y = 6.
Requires a graph!

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


3%2Ax%2B2%2Ay=6Start with the given equation



2%2Ay=6-3%2Ax Subtract 3%2Ax from both sides

y=%281%2F2%29%286-3%2Ax%29 Multiply both sides by 1%2F2

y=%281%2F2%29%286%29-%281%2F2%29%283%29x%29 Distribute 1%2F2

y=6%2F2-%283%2F2%29x Multiply

y=%28-3%2F2%29%2Ax%2B6%2F2 Rearrange the terms

y=%28-3%2F2%29%2Ax%2B3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-3%2F2 (the slope) and b=3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=%28-3%2F2%29%2A%28-4%29%2B3

y=12%2F2%2B3 Multiply

y=18%2F2 Add

y=9 Reduce

So here's one point (-4,9)



drawing%28+600%2C+600%2C+-14%2C8%2C+-4%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-2

y=%28-3%2F2%29%2A%28-2%29%2B3

y=6%2F2%2B3 Multiply

y=12%2F2 Add

y=6 Reduce

So here's another point (-2,6). Add this to our graph


drawing%28+600%2C+600%2C+-14%2C8%2C+-4%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-14%2C8%2C+-4%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-14-10%2C-1.5%2A%28-14-10%29%2B3%2C8%2B10%2C-1.5%2A%288%2B10%29%2B3%29%2C%0D%0A++++blue%28+circle%28+-2%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%28-3%2F2%29%2Ax%2B3 through the points (-4,9) and (-2,6)


So from the graph we can see that the slope is -3%2F2 (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 2 units to get to the next point), the y-intercept is (0,3)and the x-intercept is (2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,3).


So we have one point (0,3)


drawing%28+600%2C+600%2C+-10%2C12%2C+-10%2C+13%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%0D%0A++%29



Now since the slope is -3%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,3), we can go down 3 units

drawing%28++600%2C+600%2C+-10%2C12%2C+-10%2C+13%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29
and to the right 2 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C12%2C+-10%2C+13%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+2%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C0%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+0%2C+2%2C+2%2C+0%2C+180+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=%28-3%2F2%29%2Ax%2B3


drawing%28+600%2C+600%2C+-10%2C12%2C+-10%2C+13%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-1.5%2A%28-10-10%29%2B3%2C12%2B10%2C-1.5%2A%2812%2B10%29%2B3%29%2C%0D%0A++++blue%28+circle%28+2%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C0%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C3%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+3%2B%28-3%2F2%29%2C+2%2C+-3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+0%2C+2%2C+2%2C+0%2C+180+%29+%29%0D%0A++%29 So this is the graph of y=%28-3%2F2%29%2Ax%2B3 through the points (0,3) and (2,0)