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Can please someone tell me what is a slope just so I get the bigger picture of whats going on?

That means plug in x=1 (since a=1) into f = 2x^2

I got y1 = 0

y1 = -2

y1 = 2 :D **

the last one is right. y1 = 2.

so that's the answer?? y1 = 2 and I am done? Nothing else needed?

No... did you find the slope?

its 4

yes. because the derivative is 4x, evaluated at x=1 gives you 4(1) =4

So then put it in point-slope form:
y-y1 = m (x-x1)
where x1 = 1, y1= 2

yea

I did all that and I got y1 = 2 in the end, I am done ?

Wait, no, where is your x going?
y-y1 = m (x-a)
y - 2 = 4(x-1)

x-1 = 0

x = 1

x is x.

a is 1.

then why y is not y too and had to be replaced

y is y.
y-2 = 4 (x-1)

Nice! I see now! Thank you both! I wish I could give more medals!

oh i see

yes