Question

this graph shows how the number of eggs that jeanette has left is related to the number of quiches that she prepares.
number of eggs remaining
100
90
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
number of quiches
at most how many quiches can jeanette prepare if she needs to have 40 eggs left?
quiches

Explanation:

Step1: Identify the point with 40 eggs remaining

Look at the y - axis (number of eggs remaining) and find the value 40. Then, move horizontally until we meet the line on the graph.

Step2: Find the corresponding number of quiches

From the point where the number of eggs remaining is 40, move vertically down to the x - axis (number of quiches). We can see that the x - value (number of quiches) at y = 40 is 8. Wait, no, let's re - check. Wait, the initial number of eggs is 80 (when number of quiches is 0). The slope of the line: from (0,80) to (10,30), the slope $m=\frac{30 - 80}{10-0}=\frac{- 50}{10}=- 5$. The equation of the line is $y-80=-5(x - 0)$, so $y=-5x + 80$. We want to find x when $y = 40$. So, $40=-5x + 80$. Subtract 80 from both sides: $40-80=-5x$, $-40=-5x$. Divide both sides by - 5: $x = 8$? Wait, no, wait when y = 40, looking at the graph, the x - value (number of quiches) is 8? Wait, no, let's check the graph again. The y - axis is number of eggs remaining. When y = 40, the x - coordinate (number of quiches) is 8? Wait, no, let's see the grid. The line goes from (0,80) to (10,30). Let's find when y = 40. The difference in y from 80 to 40 is 40. Since the slope is - 5 (eggs per quiche), the number of quiches is $\frac{80 - 40}{5}=\frac{40}{5}=8$? Wait, no, wait 80-5x = 40, so 5x=40, x = 8. Wait, but let's check the graph. When x = 0, y = 80; x = 1, y = 75; x = 2, y = 70; x = 3, y = 65; x = 4, y = 60; x = 5, y = 55; x = 6, y = 50; x = 7, y = 45; x = 8, y = 40. Ah, there we go. So when y = 40, x = 8. Wait, but the question is "at most how many quiches can Jeanette prepare if she needs to have 40 eggs left". So when y = 40, x = 8. Wait, but let's confirm with the graph. The line passes through (0,80) and (10,30). So when y = 40, x is 8. So the number of quiches is 8? Wait, no, wait when x = 8, y = 40. So she can prepare 8 quiches and have 40 eggs left. Wait, but let's check the calculation again. The equation is $y=-5x + 80$. Set $y = 40$: $40=-5x + 80$ → $5x=80 - 40$ → $5x = 40$ → $x = 8$. So the answer is 8.

Answer:

8