Math help with graphs?

The secant y = 0.2x + 1 crosses the curve y = x^2 - 0.8x - 100

What is the equation for the tangent to the curve that is parallel with the secant?

I'm so confused. Can someone help me solve this?

1 Answer

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  • 3 weeks ago
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    For the curve, dy/dx = 2x - 0.8

    The secant has gradient 0.2, so we require when:

    2x - 0.8 = 0.2

    so, x = 0.5

    Then, y = (0.5)² - 0.8(0.5) - 100

    so, y = -100.15

    Hence, equation is y - (-100.15) = 0.2(x - 0.5)

    Then, y + 100.15 = 0.2x - 0.1

    i.e. y = 0.2x - 100.25

    :)>  

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