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Just as a note here, you don't need to use a lambda function here to get implicit plots to work. You will need to define y as a variable first, though. So, the code would be:

var('y') f = y^2-3*x-5*y+7 Yax = x Xax = y SYMAXIS = y-5/2 p1=implicit_plot(f, (x,-4, 4), (y,-2, 6)) p2= point((1/4, 5/2), size = 45, color='red') p3=implicit_plot(Yax, (x,-4, 4), (y,-2, 6),color='black') p4=implicit_plot(Xax, (x,-4, 4), (y,-2, 6),color='black') p5=implicit_plot(SYMAXIS, (x,-4, 4), (y,-2, 6),color='green') p0=p1+p2+p3+p4+p5 show(p0)

Just as a note here, you don't need to use a lambda function here to get implicit plots to work. You will need to define y as a variable first, though. So, the code would be:

 var('y')
f = y^2-3*x-5*y+7
Yax = x
Xax = y
SYMAXIS = y-5/2
p1=implicit_plot(f, (x,-4, 4), (y,-2, 6))
p2= point((1/4, 5/2), size = 45, color='red')
p3=implicit_plot(Yax,  (x,-4, 4), (y,-2, 6),color='black')
p4=implicit_plot(Xax,  (x,-4, 4), (y,-2, 6),color='black')
p5=implicit_plot(SYMAXIS,  (x,-4, 4), (y,-2, 6),color='green')
p0=p1+p2+p3+p4+p5 
show(p0)

Just as a note here, you don't need to use a lambda function here to get implicit plots to work. You will need to define y as a variable first, though. So, the code would be:

var('y')
f = y^2-3*x-5*y+7
Yax = x
Xax = y
SYMAXIS = y-5/2
p1=implicit_plot(f, (x,-4, 4), (y,-2, 6))
p2= point((1/4, 5/2), size = 45, color='red')
p3=implicit_plot(Yax,  (x,-4, 4), (y,-2, 6),color='black')
p4=implicit_plot(Xax,  (x,-4, 4), (y,-2, 6),color='black')
p5=implicit_plot(SYMAXIS,  (x,-4, 4), (y,-2, 6),color='green')
p0=p1+p2+p3+p4+p5 
show(p0)