SOLUTION: 3x - 2y = -4

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: 3x - 2y = -4      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 114056: 3x - 2y = -4
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


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



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

y=%28-1%2F2%29%28-4-3%2Ax%29 Multiply both sides by -1%2F2

y=%28-1%2F2%29%28-4%29%2B%281%2F2%29%283%29x%29 Distribute -1%2F2

y=4%2F2%2B%283%2F2%29x Multiply

y=%283%2F2%29%2Ax%2B4%2F2 Rearrange the terms

y=%283%2F2%29%2Ax%2B2 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-6

y=%283%2F2%29%2A%28-6%29%2B2

y=-18%2F2%2B2 Multiply

y=-14%2F2 Add

y=-7 Reduce

So here's one point (-6,-7)



drawing%28+600%2C+600%2C+-16%2C6%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-4

y=%283%2F2%29%2A%28-4%29%2B2

y=-12%2F2%2B2 Multiply

y=-8%2F2 Add

y=-4 Reduce

So here's another point (-4,-4). Add this to our graph


drawing%28+600%2C+600%2C+-16%2C6%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-4%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-16%2C6%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-16-10%2C1.5%2A%28-16-10%29%2B2%2C6%2B10%2C1.5%2A%286%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+-4%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-4%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%283%2F2%29%2Ax%2B2 through the points (-6,-7) and (-4,-4)


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 up 3 units and to the right 2 units to get to the next point) the y-intercept is (0,2)and the x-intercept is (-1.33333333333333,0) ,or (-4%2F3,0) . 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%2C12%2C+-8%2C+15%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 3%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,2), we can go up 3 units

drawing%28++600%2C+600%2C+-10%2C12%2C+-8%2C+15%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%283%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+-8%2C+15%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+2%2C5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C5%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+5%2C+2%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=%283%2F2%29%2Ax%2B2


drawing%28+600%2C+600%2C+-10%2C12%2C+-8%2C+15%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C1.5%2A%28-10-10%29%2B2%2C12%2B10%2C1.5%2A%2812%2B10%29%2B2%29%2C%0D%0A++++blue%28+circle%28+2%2C5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+2%2C5%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%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%282%2F2%29%2C+5%2C+2%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 So this is the graph of y=%283%2F2%29%2Ax%2B2 through the points (0,2) and (2,5)