Question

this graph shows how the amount of vegetable oil that ling has left is related to the number of cakes that she bakes.
amount of vegetable oil remaining
tablespoons of vegetable oil remaining
number of cakes
if ling bakes 2 cakes, how much vegetable oil will she have left?
3 tablespoons 2 tablespoons 4 tablespoons 7 tablespoons

Explanation:

Step1: Analyze the graph

The graph has the number of cakes on the x - axis and the amount of vegetable oil remaining (in tablespoons) on the y - axis. The line starts at (0, 10) and ends at (3, 0). We can find the equation of the line. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 10}{3 - 0}=-\frac{10}{3}\). The equation of the line is \(y - y_1=m(x - x_1)\), so \(y-10 =-\frac{10}{3}(x - 0)\), or \(y = 10-\frac{10}{3}x\).

Step2: Substitute x = 2

When \(x = 2\) (number of cakes is 2), we substitute into the equation: \(y=10-\frac{10}{3}\times2=10-\frac{20}{3}=\frac{30 - 20}{3}=\frac{10}{3}\approx3.33\). But we can also analyze the graph visually. The x - axis is number of cakes, y - axis is oil remaining. When x = 0, y = 10; when x = 3, y = 0. The line is a straight line. We can also look at the grid. Each unit on x and y. From x = 0 (y = 10) to x = 3 (y = 0), the decrease is 10 tablespoons over 3 cakes. The rate of decrease is \(\frac{10}{3}\) tablespoons per cake. After 2 cakes, the amount of oil used is \(\frac{10}{3}\times2=\frac{20}{3}\approx6.67\) tablespoons. The oil remaining is \(10-\frac{20}{3}=\frac{10}{3}\approx3.33\), which is closest to 3 tablespoons? Wait, no, maybe my initial slope calculation is wrong. Wait, maybe the graph is such that when x = 1, y = 10 - (10/3)≈6.67, x = 2, y = 10 - 2(10/3)=10 - 6.67 = 3.33, x = 3, y = 0. But looking at the options, 3 tablespoons is an option. Wait, maybe the graph is drawn with integer values. Let's check the grid. The y - axis has marks at 10,9,8,7,6,5,4,3,2,1,0. The x - axis at 0,1,2,3,4,... The line goes from (0,10) to (3,0). So when x = 2, we can see that the y - value is 10 - (10/3)2. But maybe a better way: the total oil is 10 tablespoons for 3 cakes. So per cake, oil used is 10/3. For 2 cakes, oil used is 20/3≈6.67, remaining is 10 - 6.67≈3.33, which is closest to 3? But wait, the options are 3,2,4,7. Wait, maybe I made a mistake. Wait, let's look at the graph again. The y - axis is tablespoons of vegetable oil remaining. When x = 0 (0 cakes), y = 10. When x = 1, let's see the line. At x = 1, y should be 10 - (10/3)≈6.67, x = 2, y≈3.33, x = 3, y = 0. So the closest option is 3 tablespoons? Wait, no, maybe the graph is such that the decrease is linear and we can count the grid. Let's assume the graph has a grid where each square is 1 unit. So from (0,10) to (3,0), the line passes through (1, 10 - 10/3)≈(1,6.67), (2, 10 - 20/3)≈(2,3.33), (3,0). So the value at x = 2 is approximately 3.33, which is closest to 3 tablespoons. But wait, the options have 3 tablespoons as an option.

Answer:

3 tablespoons