SOLUTION: Graph by first solving for y. 4x – 3y = 6

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Question 85070: Graph by first solving for y.
4x – 3y = 6

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


4%2Ax-3%2Ay=6Start with the given equation



-3%2Ay=6-4%2Ax Subtract 4%2Ax from both sides

y=%28-1%2F3%29%286-4%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%286%29%2B%281%2F3%29%284%29x%29 Distribute -1%2F3

y=-6%2F3%2B%284%2F3%29x Multiply

y=%284%2F3%29%2Ax-6%2F3 Rearrange the terms

y=%284%2F3%29%2Ax-2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=4%2F3 (the slope) and b=-2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-3

y=%284%2F3%29%2A%28-3%29-2

y=-12%2F3-2 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's one point (-3,-6)



drawing%28+600%2C+600%2C+-13%2C10%2C+-16%2C+8%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=0

y=%284%2F3%29%2A%280%29-2

y=0%2F3-2 Multiply

y=-6%2F3 Add

y=-2 Reduce

So here's another point (0,-2). Add this to our graph


drawing%28+600%2C+600%2C+-13%2C10%2C+-16%2C+8%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-13%2C10%2C+-16%2C+8%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-13-10%2C1.33333333333333%2A%28-13-10%29%2B-2%2C10%2B10%2C1.33333333333333%2A%2810%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%284%2F3%29%2Ax-2 through the points (-3,-6) and (0,-2)


So from the graph we can see that the slope is 4%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 4 units and to the right 3 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (1.5,0) ,or (3%2F2,0) . 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+-12%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%0D%0A++%29



Now since the slope is 4%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 up 4 units

drawing%28++600%2C+600%2C+-10%2C13%2C+-12%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-2%2B%284%2F2%29%2C+2%2C+4%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+-12%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+3%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-2%2B%284%2F2%29%2C+2%2C+4%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+2%2C+3%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=%284%2F3%29%2Ax-2


drawing%28+600%2C+600%2C+-10%2C13%2C+-12%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C1.33333333333333%2A%28-10-10%29%2B-2%2C13%2B10%2C1.33333333333333%2A%2813%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+3%2C2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-2%2B%284%2F2%29%2C+2%2C+4%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+2%2C+3%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 So this is the graph of y=%284%2F3%29%2Ax-2 through the points (0,-2) and (3,2)