All G.

asked • 06/07/25

Slope of the secant line?

Hi sorry if this seems obvious. How does one go about this and what is the formula or steps to find the secant line?

If Q is the point __ , find the slope of the secant line PQ (correct to six decimal places) for the following values of

All G.

(i) 5.9 mPQ = (ii) 5.99 mPQ = (iii) 5.999 mPQ = (iv) 5.9999 mPQ = (v) 6.1 mPQ = (vi) 6.01 mPQ = (vii) 6.001 mPQ = (viii) 6.0001 mPQ = (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, −3). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, −3).
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06/07/25

Mark M.

I shall assist once you take the time and effort to make the suggested calculations.
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06/07/25

2 Answers By Expert Tutors

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Huaizhong R. answered • 06/07/25

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Ph.D. Extensive knowledge/Experience in Math Learning/Teaching
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Given P(6, –3) on the graph of the function y=3/(5 – x). Then for any point Q other than P on the same graph, Q has the coordinates (x,y)=(x, 3/(5 – x)). To determine the slope of the secant line PQ, just use the standard formula for slope (aka difference quotient in this case)

m = rise/run = (f(x) – f(6))/(x – 6) = [(3/(5 – x) – (–3)]/(x – 6)

= (3+15 – 3x)/(5 – x)(x – 6) = 3/(x – 5).

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