Question

question 1-3
a researcher is studying the relationship between the number of tvs owned by a family and the size of the familys electric bill. after collecting data, he finds that the relationship is best modeled by the equation b = 2.43t + 95.66, where b is one months electric bill in dollars and t is the number of tvs owned by the family.
which of these is a good interpretation of the y-intercept of this model?
○ a family with no tvs has a typical electric bill of $95.66.
○ a family with no tvs has a typical electric bill of $2.43.
○ for each additional tv owned by the family, the electric bill increases by about $2.43.
○ for each additional tv owned by the family, the electric bill increases by about $95.66.

Explanation:

Step1: Recall Y - intercept meaning

The equation is \( B = 2.43T+95.66 \), where \( B \) is the electric bill and \( T \) is the number of TVs. The y - intercept occurs when \( T = 0 \) (since in the slope - intercept form \( y=mx + b \), \( x = 0 \) gives the y - intercept).

Step2: Substitute \( T = 0 \) into the equation

When \( T = 0 \), we have \( B=2.43\times0 + 95.66=95.66 \). This means when the number of TVs (\( T \)) is 0 (a family with no TVs), the electric bill (\( B \)) is $95.66.

Let's analyze the other options:

• Option 3: The slope is 2.43, which represents the change in \( B \) for a unit change in \( T \). So the bill increases by $2.43 per TV, not $2.43 for no TVs. So this is incorrect.
• Option 4: The slope is 2.43, so the bill increases by $2.43 per TV, not $95.66. So this is incorrect.
• Option 5: The slope is 2.43, so the bill increases by $2.43 per TV, not $95.66. So this is incorrect.

Answer:

A family with no TVs has a typical electric bill of $95.66. (The first option among the given options, assuming the options are ordered as: 1. A family with no TVs has a typical electric bill of $95.66, 2. A family with no TVs has a typical electric bill of $2.43, 3. For each additional TV owned by the family, the electric bill increases by about $2.43, 4. For each additional TV owned by the family, the electric bill increases by about $95.66)