Question

Melanie and Tracy are each finding the equation of the trend line that fits the data in the table below. 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?

Answer 1

Melanie: (2010, 48) and (2013, 59)
Equation will be
y = (59-48)/(2013-2010) * (x - 2010) + 48
>> y = (11/3) * (x - 2010) + 48
>> y = (11/3)x - (11/3)*2010 + 48
>> y = (11/3)x - 7370 + 48
>> y = (11/3)x - 7322

Tracy: (0, 48) and (3, 59)
Equation will be
y = (59-48)/(3-0) * (x - 0) + 48
>> y = (11/3) * x + 48
>> y = (11/3)x + 48

The slopes of both the equations are same, but y-intercept are different. Because Melanie used actual years (variable x), whereas Tracy used years since 2010.