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Select all the statements that are true for the linear equation.%0D%0A%0D%0A(4 points)%0D%0AResponses%0D%0A%0D%0Ay = 0.03x + 0.55 represents the linear equation%0D%0Ay = 0.03x + 0.55 represents the linear equation%0D%0A%0D%0AThe cost of a loaf of bread in 1990 was $0.70.%0D%0AThe cost of a loaf of bread in 1990 was $0.70.%0D%0A%0D%0A(27,1.48) is a solution to the linear equation%0D%0A(27,1.48) is a solution to the linear equation%0D%0A%0D%0AThe cost of a loaf of bread in 2015 was $1.50%0D%0AThe cost of a loaf of bread in 2015 was $1.50%0D%0A%0D%0A(5, 0.7) is a solution to the linear equation%0D%0A(5, 0.7) is a solution to the linear equation%0D%0A%0D%0AA loaf of bread cost $0.55 in 1985

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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.
  3. (5, 0.7) is a solution to the linear equation.
  4. A loaf of bread cost $0.55 in 1985.