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Answer :
To determine which function best models the relationship between the number of months since the start of the build and the percentage of the house left to build, we can analyze the given data points and compare them to the provided linear equations.
Step 1: Analyze the Data
We have the following data points that show the relationship between months and the percentage of the house left to build:
- (0, 100)
- (1, 86)
- (2, 65)
- (3, 59)
- (4, 41)
- (5, 34)
Step 2: Understand the Task
Our objective is to find a linear function [tex]\( y = mx + b \)[/tex] where:
- [tex]\( x \)[/tex] is the number of months since the start,
- [tex]\( y \)[/tex] is the percentage of the house left to build.
Step 3: Compare with Given Options
We are given four potential functions:
- (A) [tex]\( y = -13.5x + 97.8 \)[/tex]
- (B) [tex]\( y = -13.5x + 7.3 \)[/tex]
- (C) [tex]\( y = 97.8x - 13.5 \)[/tex]
- (D) [tex]\( y = 7.3x - 97.8 \)[/tex]
Step 4: Analyze the Options
From calculations, the best fit line for this data is approximately:
- Slope ([tex]\( m \)[/tex]): -13.46
- Intercept ([tex]\( b \)[/tex]): 97.81
Now, let's match these values with the options:
- Option A: [tex]\( y = -13.5x + 97.8 \)[/tex]
- Slope: -13.5
- Intercept: 97.8
This option closely matches the calculated values, with a slope of -13.5 and an intercept of 97.8.
Thus, the function [tex]\( y = -13.5x + 97.8 \)[/tex] (Option A) is the best model for the data, correctly reflecting the trend in the percentage of the house left to build over the months.
Step 1: Analyze the Data
We have the following data points that show the relationship between months and the percentage of the house left to build:
- (0, 100)
- (1, 86)
- (2, 65)
- (3, 59)
- (4, 41)
- (5, 34)
Step 2: Understand the Task
Our objective is to find a linear function [tex]\( y = mx + b \)[/tex] where:
- [tex]\( x \)[/tex] is the number of months since the start,
- [tex]\( y \)[/tex] is the percentage of the house left to build.
Step 3: Compare with Given Options
We are given four potential functions:
- (A) [tex]\( y = -13.5x + 97.8 \)[/tex]
- (B) [tex]\( y = -13.5x + 7.3 \)[/tex]
- (C) [tex]\( y = 97.8x - 13.5 \)[/tex]
- (D) [tex]\( y = 7.3x - 97.8 \)[/tex]
Step 4: Analyze the Options
From calculations, the best fit line for this data is approximately:
- Slope ([tex]\( m \)[/tex]): -13.46
- Intercept ([tex]\( b \)[/tex]): 97.81
Now, let's match these values with the options:
- Option A: [tex]\( y = -13.5x + 97.8 \)[/tex]
- Slope: -13.5
- Intercept: 97.8
This option closely matches the calculated values, with a slope of -13.5 and an intercept of 97.8.
Thus, the function [tex]\( y = -13.5x + 97.8 \)[/tex] (Option A) is the best model for the data, correctly reflecting the trend in the percentage of the house left to build over the months.
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