Liz and Sara are making cookies for a bake sale. The graph shows the number of cookies that Liz bakes during a 5-hour period.

Graph in the coordinate plane with title cookies baked by Liz. Vertical axis goes from 0 to 220 in increments of 10 and is labeled number of cookies baked. Horizontal axis goes from 0 to 5 in increments of 1 and is labeled time in hours. A ray on the graph starts at point begin ordered pair 0 comma 19 end ordered pair and goes through point begin ordered pair 4 comma 179 end ordered pair.



The equation y = 45x + 38 shows the number of cookies that Sara bakes during the same hours with y representing the number of cookies and x representing the number of hours.

Which statements about the cookie baking by the two girls are true?

Select each correct answer.



Responses

Sara had baked more cookies at the start of the 5 hours than Liz.
Sara had baked more cookies at the start of the 5 hours than Liz.

Sara bakes 45 cookies each hour.
Sara bakes 45 cookies each hour.

Liz bakes 19 cookies each hour.
Liz bakes 19 cookies each hour.

Liz bakes more cookies each hour than Sara.

1 answer

To analyze the statements regarding Liz and Sara's cookie baking, let's consider the details provided.

  1. Sara had baked more cookies at the start of the 5 hours than Liz.

    • To determine this, we check the number of cookies each girl baked at the start (x = 0).
    • From the information given, when x = 0, the equation for Sara is: \[ y = 45(0) + 38 = 38 \]
    • For Liz, the graph indicates that at x = 0, y = 19.
    • Since 38 > 19, this statement is true.
  2. Sara bakes 45 cookies each hour.

    • The equation for Sara's cookie baking is \(y = 45x + 38\). The slope (45) indicates the number of cookies baked per hour. Therefore, this statement is also true.
  3. Liz bakes 19 cookies each hour.

    • To find Liz's baking rate, we note that the graph shows she starts at 19 cookies and moves to 179 cookies over 4 hours (the change is 179 - 19 = 160 cookies over a span of 4 hours).
    • Therefore, her rate is: \[ \text{Rate} = \frac{160 \text{ cookies}}{4 \text{ hours}} = 40 \text{ cookies per hour}. \]
    • Since she bakes 40 cookies per hour, this statement is false.
  4. Liz bakes more cookies each hour than Sara.

    • From our previous calculations, Liz bakes 40 cookies per hour, while Sara bakes 45 cookies per hour.
    • Since 40 < 45, this statement is false.

In summary, the correct true statements are:

  • Sara had baked more cookies at the start of the 5 hours than Liz.
  • Sara bakes 45 cookies each hour.