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Bot GPT 4-o mini To determine which statements are true for the linear equation \( y = 0.03x + 0.55 \), we need to analyze each statement:
1. **y = 0.03x + 0.55 represents the linear equation.**
- True, this is a valid linear equation in slope-intercept form.
2. **The cost of a loaf of bread in 1990 was $0.70.**
- To find the year 1990's corresponding \( x \) value in the context of the equation, we need to know the base year. If we assume that \( x \) represents the number of years since 1985, then \( x = 1990 - 1985 = 5 \). Let's calculate:
\[
y = 0.03(5) + 0.55 = 0.15 + 0.55 = 0.70
\]
This statement is true.
3. **(27,1.48) is a solution to the linear equation.**
- Let's substitute \( x = 27 \) into the equation:
\[
y = 0.03(27) + 0.55 = 0.81 + 0.55 = 1.36
\]
Since \( y = 1.36 \) and not \( 1.48 \), this statement is false.
4. **The cost of a loaf of bread in 2015 was $1.50.**
- For 2015, we assume \( x = 2015 - 1985 = 30 \):
\[
y = 0.03(30) + 0.55 = 0.90 + 0.55 = 1.45
\]
This is not equal to $1.50, so this statement is false.
5. **(5, 0.7) is a solution to the linear equation.**
- We check by substituting \( x = 5 \):
\[
y = 0.03(5) + 0.55 = 0.15 + 0.55 = 0.70
\]
This is true.
6. **A loaf of bread cost $0.55 in 1985.**
- For 1985, \( x = 0 \):
\[
y = 0.03(0) + 0.55 = 0.55
\]
This statement is true.
In conclusion, the true statements are:
1. y = 0.03x + 0.55 represents the linear equation.
2. The cost of a loaf of bread in 1990 was $0.70.
5. (5, 0.7) is a solution to the linear equation.
6. A loaf of bread cost $0.55 in 1985.