Question

fernando is passionate about movies and dreams of going to film school. his goal for the next year is to watch every movie that won the academy award for best picture. hes already seen some of them and now plans to watch one per week until hes seen them all. this table shows the relationship between how long (in weeks) fernando has followed his plan, x, and the number of best picture winners he has seen, y. x (weeks) y (best picture winners) 9 16 17 24 19 26 28 35 according to the values in the table, do x and y have a proportional relationship? yes no

Explanation:

Step1: Recall proportional - relationship condition

For two variables \(x\) and \(y\) to have a proportional relationship, the ratio \(\frac{y}{x}\) must be constant for all non - zero values of \(x\).

Step2: Calculate ratios for each pair

For the first pair \((x = 9,y = 16)\), \(\frac{y}{x}=\frac{16}{9}\approx1.78\).
For the second pair \((x = 17,y = 24)\), \(\frac{y}{x}=\frac{24}{17}\approx1.41\).
For the third pair \((x = 19,y = 26)\), \(\frac{y}{x}=\frac{26}{19}\approx1.37\).
For the fourth pair \((x = 28,y = 35)\), \(\frac{y}{x}=\frac{35}{28}=\frac{5}{4} = 1.25\).

Step3: Check constancy of ratios

Since \(\frac{16}{9}
eq\frac{24}{17}
eq\frac{26}{19}
eq\frac{35}{28}\), the ratio \(\frac{y}{x}\) is not constant.

Answer:

no