Which table matches the relationship between 𝑥 and 𝑦 shown in the graph? Is it A), with coordinate pairs five, zero; 10, five; and 15, 10? B) 10, five; 15, 10; 20, 25? C) Zero, five; five, 10; 10, 15? D) Five, 10; 10, 15; 15, 20? Or E) five, five; 10, 10; 15, 15?
There are five points marked on the graph. These can be written as a coordinate pair 𝑥, 𝑦. We go along the corridor and then up the stairs so the 𝑥-coordinate comes first. The first point has coordinates five, zero. The second coordinate is 10, five. The third point has coordinates 15, 10. The fourth point is 20, 15. And finally, the fifth point has coordinates 25, 20.
We notice that in each pair, the 𝑦-coordinate is five less than the 𝑥-coordinate. This means that the straight line would have equation 𝑦 equals 𝑥 minus five. We need to find which of the five tables correspond to these points. All three of the points in table A — five, zero; 10, 5; and 15, 10 — lie on the line. This means that table A matches the relationship between 𝑥 and 𝑦 shown in the graph.
We now need to check whether any of the other tables are also correct. Table B has two correct points, 10, five and 15, 10. The point 20, 25 does not lie on the graph. Table C has no correct points, as zero, five; five, 10; and 10, 15 do not lie on the graph. The same is true for table D. Five, 10; 10, 15; and 15, 20 are not on the graph.
In both of these tables, the 𝑦-coordinate is five more instead of five less than the 𝑥-coordinate. In table E, the 𝑥- and 𝑦-coordinates are the same, five, five; 10, 10; and 15, 15. This means that this does not match the relationship on the graph. The correct answer is table A.