SOLUTION: Graph the equation. 2x + 3y = 6

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Question 111919This question is from textbook Beginning Algebra
: Graph the equation.
2x + 3y = 6
This question is from textbook Beginning Algebra

Answer by jim_thompson5910(14872) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B3%2Ay=6Start with the given equation



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

y=%281%2F3%29%286-2%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%286%29-%281%2F3%29%282%29x%29 Distribute 1%2F3

y=6%2F3-%282%2F3%29x Multiply

y=%28-2%2F3%29%2Ax%2B6%2F3 Rearrange the terms

y=%28-2%2F3%29%2Ax%2B2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-2%2F3 (the slope) and b=2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-9

y=%28-2%2F3%29%2A%28-9%29%2B2

y=18%2F3%2B2 Multiply

y=24%2F3 Add

y=8 Reduce

So here's one point (-9,8)



drawing%28+600%2C+600%2C+-19%2C4%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-6

y=%28-2%2F3%29%2A%28-6%29%2B2

y=12%2F3%2B2 Multiply

y=18%2F3 Add

y=6 Reduce

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


drawing%28+600%2C+600%2C+-19%2C4%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-6%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-19%2C4%2C+-4%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-19-10%2C-0.666666666666667%2A%28-19-10%29%2B2%2C4%2B10%2C-0.666666666666667%2A%284%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+-6%2C6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-9%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%28-2%2F3%29%2Ax%2B2 through the points (-9,8) and (-6,6)


So from the graph we can see that the slope is -2%2F3 (which tells us that in order to go from point to point we have to start at one point and go down -2 units and to the right 3 units to get to the next point), the y-intercept is (0,2)and the x-intercept is (3,0) . So all of this information verifies our graph.


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)


drawing%28+600%2C+600%2C+-10%2C13%2C+-10%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.1%2C+1.5+%29+%29%0D%0A++%29



Now since the slope is -2%2F3, 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 2 units

drawing%28++600%2C+600%2C+-10%2C13%2C+-10%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29
and to the right 3 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C13%2C+-10%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+3%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C0%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+0%2C+3%2C+2%2C+0%2C+180+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=%28-2%2F3%29%2Ax%2B2


drawing%28+600%2C+600%2C+-10%2C13%2C+-10%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-0.666666666666667%2A%28-10-10%29%2B2%2C13%2B10%2C-0.666666666666667%2A%2813%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+3%2C0%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C0%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%28-2%2F2%29%2C+2%2C+-2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+0%2C+3%2C+2%2C+0%2C+180+%29+%29%0D%0A++%29 So this is the graph of y=%28-2%2F3%29%2Ax%2B2 through the points (0,2) and (3,0)