Select all the statements that are true for the linear equation.

Question

(4 points)
Responses

y = 0.03x + 0.55 represents the linear equation
y = 0.03x + 0.55 represents the linear equation

The cost of a loaf of bread in 1990 was $0.70.
The cost of a loaf of bread in 1990 was $0.70.

(27,1.48) is a solution to the linear equation
(27,1.48) is a solution to the linear equation

The cost of a loaf of bread in 2015 was $1.50
The cost of a loaf of bread in 2015 was $1.50

(5, 0.7) is a solution to the linear equation
(5, 0.7) is a solution to the linear equation

A loaf of bread cost $0.55 in 1985

Answer 1

Let's evaluate each statement in relation to the given linear equation \( y = 0.03x + 0.55 \).

1. y = 0.03x + 0.55 represents the linear equation:

   • True. This is indeed a linear equation in slope-intercept form.

2. The cost of a loaf of bread in 1990 was $0.70:

   • To determine if this is true, we need to find the value of \( x \) that corresponds to the year 1990. If we assume \( x = 0 \) is 1980, then \( x = 10 \) would be 1990. Plugging \( x = 10 \) into the equation: \[ y = 0.03(10) + 0.55 = 0.3 + 0.55 = 0.85 \]
   • This is not $0.70, so this statement is False.

3. (27, 1.48) is a solution to the linear equation:

   • Substitute \( x = 27 \) into the equation: \[ y = 0.03(27) + 0.55 = 0.81 + 0.55 = 1.36 \]
   • Since \( 1.36 \neq 1.48 \), this statement is False.

4. The cost of a loaf of bread in 2015 was $1.50:

   • For 2015, \( x = 35 \) (assuming \( x = 0 \) is 1980): \[ y = 0.03(35) + 0.55 = 1.05 + 0.55 = 1.60 \]
   • This is not $1.50, thus the statement is False.

5. (5, 0.7) is a solution to the linear equation:

   • Substitute \( x = 5 \) into the equation: \[ y = 0.03(5) + 0.55 = 0.15 + 0.55 = 0.70 \]
   • Since \( (5, 0.7) \) satisfies the equation, this statement is True.

6. A loaf of bread cost $0.55 in 1985:

   • For 1985, \( x = 5 \): \[ y = 0.03(5) + 0.55 = 0.15 + 0.55 = 0.70 \]
   • This does not support the claim that it was $0.55. So this statement is False.

Summary of True Statements:

• True:

  • y = 0.03x + 0.55 represents the linear equation
  • (5, 0.7) is a solution to the linear equation

• False:

  • The cost of a loaf of bread in 1990 was $0.70
  • (27, 1.48) is a solution to the linear equation
  • The cost of a loaf of bread in 2015 was $1.50
  • A loaf of bread cost $0.55 in 1985.

Thus, the true statements are:

• y = 0.03x + 0.55 represents the linear equation.
• (5, 0.7) is a solution to the linear equation.

Answer 2

Which of the following types of measurement would need a discrete data (whole number) constraint?(1 point)
Option #
would need a whole number constraint.

Answer 3

Discrete data is typically characterized by countable values, which means that the values must be whole numbers (integers). Examples of measurements that require a whole number constraint include:

• The number of students in a classroom.
• The number of cars in a parking lot.
• The number of votes received in an election.
• The number of items sold in a store.

If you provide specific options or examples, I can help identify which specific option would require a whole number constraint. Without specific options, the general answer is that any measurement that involves counting distinct objects or events would typically need a discrete data constraint.