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Find the equation of the tangent line to the curve $y=x^2-1$ parallel to the line $2x+y=6$.

Hello, can someone can help me with this? Thank you. ;)

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Since the slope of line $2x+y=6$ is $-2$, we left to find the derivative of $y=x^2-1$, which is $y'=2x$, and put $-2$ instead of $y'$(why we do that?).

$$-2=2x$$

$$x=-1$$

Substituting $x=-1$ into $y=x^2-1$ we get $y=0$, and we have a point $(-1,0)$ with a slope $m=-2$. Can you proceed from here?

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  • $\begingroup$ Hey, thank you for responding. I am stuck in the point (-1,0), and i really dont know what to do next. $\endgroup$ – Chryss Tiquison Sep 5 '13 at 15:14
  • $\begingroup$ Use the line equation formula: $y-y_1=m(x-x_1)$ and put $x_1=-1$, $y_1=0$ and $m=-2$. What you get? $\endgroup$ – Salech Rubenstein Sep 5 '13 at 15:17
  • $\begingroup$ Ill comment my answer in few minutes $\endgroup$ – Chryss Tiquison Sep 5 '13 at 15:23
  • $\begingroup$ Is the answer y= 2x + 2 ? $\endgroup$ – Chryss Tiquison Sep 5 '13 at 15:32
  • $\begingroup$ No, that is not the answer. Two lines are parallel if they have the same slope. But your equation is with slope $2$. $\endgroup$ – Salech Rubenstein Sep 5 '13 at 15:36
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HINT:

The slope of the line $2x+y=6$ is $-2$. Two lines are parallel if they have the same slope. What construction in calculus gives you the slope of a tangent line to a point on the graph?

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