Alright, let's solve it step-by-step.
We are given a ratio of nuts to pieces of dried fruit as 3:1. This means for every 3 nuts, there is 1 piece of dried fruit.
Now let's fill in the ratio table step by step to show equivalent ratios:
### Step-by-Step Calculation:
1. First Ratio:
- Nuts: 3
- Fruit: 1
The first pair is already given in the table.
2. Second Ratio:
- Nuts: 6
- Fruit: 2
The second pair is already given in the table.
3. Third Ratio:
- By maintaining the ratio 3:1, if we increase the number of nuts by another set of 3 (from the first ratio), we get 3 + 3 = 6 nuts. Since this is already our second set, let's do it again:
- Nuts: 6 + 3 = 9
- Fruit: 2 + 1 = 3
So, the third pair is (9, 3).
4. Fourth Ratio:
- Again, maintaining the 3:1 ratio,
- Nuts: 9 + 3 = 12
- Fruit: 3 + 1 = 4
So, the fourth pair is (12, 4).
5. Fifth Ratio:
- Continuing with the same ratio,
- Nuts: 12 + 3 = 15
- Fruit: 4 + 1 = 5
So, the fifth pair is (15, 5).
Now the completed ratio table should look like this:
[tex]\[
\begin{tabular}{|c|c|}
\hline Nuts $(x)$ & Fruit $(y)$ \\
\hline 3 & 1 \\
\hline 6 & 2 \\
\hline 9 & 3 \\
\hline 12 & 4 \\
\hline 15 & 5 \\
\hline
\end{tabular}
\][/tex]
### Graphing on the Coordinate Plane:
To graph these ratios, plot the points on a coordinate plane with the number of nuts on the x-axis and the number of pieces of dried fruit on the y-axis. The points to plot are:
- (3, 1)
- (6, 2)
- (9, 3)
- (12, 4)
- (15, 5)
These points will lie in a straight line, demonstrating the constant ratio relationship between the number of nuts and pieces of dried fruit.
