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# Name:Makayla Roberts
# I worked on this code with: Sonia

# Please do all of your work for this week's lab in this worksheet. If
# you wish to create other worksheets for scratch work, you can, but
# this is the one that will be graded. You do not need to do anything
# to turn in your lab. It will be collected by your TA at the beginning
# of (or right before) next week’s lab.

# Be sure to clearly label which question you are answering as you go and to
# use enough comments that you and the grader can understand your code.


In [3]:
#1
var ("x,y")
plot3d(3*x + 5*y, (x, -5,5), (y, -5,5), aspect_ratio= [1,1,.1])

In [2]:
#2
#when y=0, f(x,y)= x^2+ y^2 just becomes f(x,y)= x^2. The tangent line is y=0
plot (x^2, axes_labels= ["X", "Z"]) + plot (0, color="red", thickness=3)

In [3]:
#3
var ("x,y")
plot (y^2, axes_labels=["Y", "Z"]) + plot (0, color="red", thickness=3)

In [4]:
#4
var ("x,y")
z=0*x+0*y
plot3d(x^2+ y^2, (x, -5,5), (y, -5,5), aspect_ratio= [1,1,.1]) + plot3d (0, (x, -5,5), (y, -5,5), color="red")

In [5]:
#5
var ("x,y")
z= 2*(x-2)-1*(y-3)-7
plot3d (2*(x-2)-1*(y-3)-7, (x, -20,20), (y, -20,20), color="red", opacity= .5) + point3d ([2,3,-7], aspect_ratio= [1,1,.1], size= 10, color= "black")

In [6]:
#6
var ("x,y")
z= 2*(x-1) -2*(y+1) +2
plot3d(x^2+ y^2, (x, -5,5), (y, -5,5), aspect_ratio= [1,1,.1], opacity=.5)+ plot3d (2*(x-1) -2*(y+1) +2, (x, -5,5), (y, -5,5), color="red", opacity= .5) + point3d ([1,-1,2], color="black", size=10)