Question

this graph shows how the number of glasses that rita has left is related to the number of tables that she has set. number of glasses remaining 1,000 800 600 400 200 0 200 400 600 800 1,000 number of tables if rita sets 700 tables, how many glasses will she have left? 300 glasses 400 glasses 500 glasses 200 glasses

Explanation:

Step1: Analyze the graph

The graph is a linear graph showing the relationship between the number of tables set and the number of glasses remaining. The x - axis is the number of tables (from 0 to 1000) and the y - axis is the number of glasses remaining (from 0 to 1000). The line starts at (0, 900) approximately (since at 0 tables, glasses remaining are between 800 and 1000, closer to 900) and ends at (900, 0) approximately. The slope of the line can be calculated, but we can also use the grid to find the value at x = 700.

Step2: Locate x = 700 on the x - axis

Find the point on the x - axis where the number of tables is 700. Then, move up until we intersect the line representing the number of glasses remaining. From the graph, when the number of tables is 700, we look at the y - value (number of glasses remaining). By observing the grid, each grid square on the x - axis and y - axis seems to represent 100 units (since from 0 to 200 is 2 grid squares, so 100 per square). At x = 0, y = 900; at x = 900, y = 0. The equation of the line can be thought of as \(y=-\frac{900}{900}x + 900=-x + 900\) (since it's a linear relationship with slope - 1 and y - intercept 900). When x = 700, \(y=-700 + 900 = 200\)? Wait, no, maybe my initial y - intercept was wrong. Wait, looking at the graph again, when x = 0, the y - value is 900? Wait, no, the first grid line above 800 is 900? Wait, the y - axis has 800, 600, 400, 200. Wait, maybe the y - intercept is 900? Wait, no, let's check the points. When x = 0, the number of glasses remaining is 900 (between 800 and 1000). When x = 100, y = 800? Wait, no, the line goes from (0, 900) to (900, 0). So the slope is \(\frac{0 - 900}{900-0}=- 1\). So the equation is \(y=-x + 900\). When x = 700, \(y=-700 + 900 = 200\)? But wait, the options have 200 glasses as one of the options. Wait, but let's check the graph again. Wait, maybe I misread the y - intercept. Wait, the graph's y - axis at x = 0: the point is at 900? Wait, the first mark on the y - axis is 800, then 1000 at the top. Wait, maybe the y - intercept is 900, and the line goes to (900, 0). So when x = 700, y = 900 - 700 = 200. So the number of glasses remaining is 200? Wait, but let's check the options. The options are 300, 400, 500, 200. So 200 is an option.

Answer:

200 glasses (the option with "200 glasses")