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To determine the unit rate of change of flour with respect to sugar from the given data, we can start by calculating the ratios of flour to sugar for each batch.
### Step 1: Convert Mixed Numbers to Improper Fractions or Decimals
First, let's convert the mixed numbers for flour into improper fractions or decimals.
- Batch 1: [tex]\( 4 \frac{1}{2} = 4 + \frac{1}{2} = 4.5 \)[/tex]
- Batch 2: [tex]\( 6 \frac{3}{4} = 6 + \frac{3}{4} = 6.75 \)[/tex]
- Batch 3: [tex]\( 9 \)[/tex]
### Step 2: Calculate the Ratios
Next, we compute the ratio of flour to sugar for each batch:
- Batch 1: [tex]\( \frac{4.5}{2} = 2.25 \)[/tex]
- Batch 2: [tex]\( \frac{6.75}{3} = 2.25 \)[/tex]
- Batch 3: [tex]\( \frac{9}{4} = 2.25 \)[/tex]
### Step 3: Determine the Unit Rate
Since the ratio is consistent across all batches, the unit rate of change of flour with respect to sugar is:
[tex]\[ \text{Unit rate} = 2.25 \][/tex]
This means that for every 1 cup of sugar, there are 2.25 cups of flour.
### Step 4: Graph the Relationship
To graph the proportional relationship, we plot the data points (cups of sugar, cups of flour), which are:
- [tex]\( (2, 4.5) \)[/tex]
- [tex]\( (3, 6.75) \)[/tex]
- [tex]\( (4, 9) \)[/tex]
Since the relationship is proportional, all points should lie on a line that passes through the origin (0, 0). The line's slope corresponds to the unit rate we calculated.
Steps to plot the graph:
1. Draw the x-axis (cups of sugar) and y-axis (cups of flour).
2. Mark points (2, 4.5), (3, 6.75), and (4, 9) on the graph.
3. Draw a straight line passing through these points and the origin (0, 0).
### Step 5: Draw and Label the Graph
- X-axis: Labeled as "Cups of Sugar".
- Y-axis: Labeled as "Cups of Flour".
- Plot: Points [tex]\((2, 4.5)\)[/tex], [tex]\((3, 6.75)\)[/tex], and [tex]\((4, 9)\)[/tex].
- Line: A straight line passing through the origin and these points, illustrating the proportional relationship.
To summarize, the unit rate of change of flour with respect to sugar is [tex]\(2.25\)[/tex]. The graph should portray a straight line through (0,0), (2, 4.5), (3, 6.75), and (4, 9), illustrating the consistent ratio.
### Step 1: Convert Mixed Numbers to Improper Fractions or Decimals
First, let's convert the mixed numbers for flour into improper fractions or decimals.
- Batch 1: [tex]\( 4 \frac{1}{2} = 4 + \frac{1}{2} = 4.5 \)[/tex]
- Batch 2: [tex]\( 6 \frac{3}{4} = 6 + \frac{3}{4} = 6.75 \)[/tex]
- Batch 3: [tex]\( 9 \)[/tex]
### Step 2: Calculate the Ratios
Next, we compute the ratio of flour to sugar for each batch:
- Batch 1: [tex]\( \frac{4.5}{2} = 2.25 \)[/tex]
- Batch 2: [tex]\( \frac{6.75}{3} = 2.25 \)[/tex]
- Batch 3: [tex]\( \frac{9}{4} = 2.25 \)[/tex]
### Step 3: Determine the Unit Rate
Since the ratio is consistent across all batches, the unit rate of change of flour with respect to sugar is:
[tex]\[ \text{Unit rate} = 2.25 \][/tex]
This means that for every 1 cup of sugar, there are 2.25 cups of flour.
### Step 4: Graph the Relationship
To graph the proportional relationship, we plot the data points (cups of sugar, cups of flour), which are:
- [tex]\( (2, 4.5) \)[/tex]
- [tex]\( (3, 6.75) \)[/tex]
- [tex]\( (4, 9) \)[/tex]
Since the relationship is proportional, all points should lie on a line that passes through the origin (0, 0). The line's slope corresponds to the unit rate we calculated.
Steps to plot the graph:
1. Draw the x-axis (cups of sugar) and y-axis (cups of flour).
2. Mark points (2, 4.5), (3, 6.75), and (4, 9) on the graph.
3. Draw a straight line passing through these points and the origin (0, 0).
### Step 5: Draw and Label the Graph
- X-axis: Labeled as "Cups of Sugar".
- Y-axis: Labeled as "Cups of Flour".
- Plot: Points [tex]\((2, 4.5)\)[/tex], [tex]\((3, 6.75)\)[/tex], and [tex]\((4, 9)\)[/tex].
- Line: A straight line passing through the origin and these points, illustrating the proportional relationship.
To summarize, the unit rate of change of flour with respect to sugar is [tex]\(2.25\)[/tex]. The graph should portray a straight line through (0,0), (2, 4.5), (3, 6.75), and (4, 9), illustrating the consistent ratio.
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