The point P(4, −2) lies on the curve y = 2/(3 − x). (a) If Q is the point (x, 2/(3 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 mPQ = (ii) 3.99 mPQ = (iii) 3.999 mPQ = (iv) 3.9999 mPQ = (v) 4.1 mPQ = (vi) 4.01 mPQ = (vii) 4.001 mPQ = (viii) 4.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, −2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, −2).

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.