Question

Nathaniel purchases a one year membership pass to an art museum as a member he receives a discounted entrance fee the total cost for the year f(x) after c visits to the art museum is shown on the graph below

Answer 1

For this case, we must find the equation of the line.
 The generic equation of the line is:
 $y-yo = m (x-xo)$
 The slope of the line is:
 $m = \frac{y2-y1}{x2-x1}$
 Substituting values we have:
 $m = \frac{15-12}{2-0}$
 Rewriting:
 $m = \frac{3}{2}$
 $m = 1.5$
 We now choose an ordered pair:
 (xo, yo) = (0, 12)
 Substituting values we have:
 $y-12 = 1.5 (x-0)$
 Rewriting the equation:
 $y= 1.5x+12$
 For 20 visits, we evaluate the equation when x = 20.
 We have then:
 $y= 1.5(20)+12$
 $y= 30+12$
 $y= 42$
 Answer:
 The discounted entrance fee is 1.5$. The total cost is 42$ after 20 visits

Answer 2

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