How do you graph #9x-3y=-9# using the intercepts?

Answer 1

See below:

When using intercepts, remember that the the #x#-intercept will be in the form of #(x,0)# and the #y#-intercept will be in the form of #(0,y)#, where the #x# and #y# in the points are the intercepts.

We can use this to find the intercepts in our equation #9x-3y=-9#.

x intercept

Set #y=0#:

#9x-3(0)=-9#

#9x=-9#

#x=-1 => (-1,0)#

y intercept

Set #x=0#

#9(0)-3y=-9#

#-3y=-9#

#y=3 => (0,3)#

Graph

Let's plot those points:

graph{((x+1)^2+(y-0)^2-.5^2)((x-0)^2+(y-3)^2-.5^2)=0}

and now connect them up:

graph{((x+1)^2+(y-0)^2-.5^2)((x-0)^2+(y-3)^2-.5^2)(9x-3y+9)=0}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.