SOLUTION: Plot the graph f(x)=3x - 2

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Question 115540: Plot the graph
f(x)=3x - 2

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=3%2Ax-2 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%29-2

y=-6-2 Multiply

y=-8 Add

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


drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-1

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

y=-3-2 Multiply

y=-5 Add

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


drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-12-10%2C3%2A%28-12-10%29%2B-2%2C9%2B10%2C3%2A%289%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=3%2Ax-2 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 up 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)


drawing%28+600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%0D%0A++%29


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 up 3 units


drawing%28++600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%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 1 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%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+%281%2F2%29%2C+1%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29
Now draw a line through those points to graph y=3%2Ax-2


drawing%28+600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C3%2A%28-10-10%29%2B-2%2C11%2B10%2C3%2A%2811%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%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+%281%2F2%29%2C+1%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 So this is the graph of y=3%2Ax-2 through the points (0,-2) and (1,1)