Question

melanie and tracy are each finding the equation of the trend line that fits the data in the table below.

participation in the school band
year | number of students
2010 | 48
2011 | 52
2012 | 55
2013 | 59

melanie uses the ordered pairs (2010, 48) and (2013, 59) to find her equation. tracy defines x as the number of years since 2010 and uses the ordered pairs (0, 48) and (3, 59) to find her equation. how will the two girls equations compare?

they will have the same slopes and the same y-intercepts.
they will have the same slopes but different y-intercepts.
they will have different slopes but the same y-intercepts.
they will have different slopes and different y-intercepts.

Explanation:

Calculate and compare the slopes

$$
LATEXBLOCK0
$$

Calculate and compare the y-intercepts

$$
LATEXBLOCK1
$$

Determine the correct relationship

$$
LATEXBLOCK2
$$

Answer:

• (A) They will have the same slopes and the same y-intercepts.
• (B) They will have the same slopes but different y-intercepts. (Correct answer)
• (C) They will have different slopes but the same y-intercepts.
• (D) They will have different slopes and different y-intercepts.