SOLUTION: -3x-y=2 sketch the graph of each equation

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Question 91356: -3x-y=2 sketch the graph of each equation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


-3%2Ax-1%2Ay=2Start with the given equation



-1%2Ay=2%2B3%2Ax Add 3%2Ax to both sides

y=%28-1%29%282%2B3%2Ax%29 Multiply both sides by -1

y=%28-1%29%282%29%2B%281%29%28-3%29x%29 Distribute -1

y=-2-%283%29x Multiply

y=-3%2Ax-2 Rearrange the terms

y=-3%2Ax-2 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-3

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

y=9-2 Multiply

y=7 Add

So here's one point (-3,7)





Now lets find another point

Plug in x=-2

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

y=6-2 Multiply

y=4 Add

So here's another point (-2,4). Add this to our graph





Now draw a line through these points

So this is the graph of y=-3%2Ax-2 through the points (-3,7) and (-2,4)


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 down -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) . 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)






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 down 3 units


and to the right 1 units to get to our next point



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


So this is the graph of y=-3%2Ax-2 through the points (0,-2) and (1,-5)