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.

Answer 1

The answer is B.They will have the same slopes but different y-intercepts.

Step-by-step explanation:

Answer 2

They will have the same slopes but different y-intercepts.

Step-by-step explanation:

Slope of the line = change in y coordinate/change in x coordinate

The first student Melaine has used (2010,48) and (2013,59)

Hence slope = change in y/change inx = (59-48)/(2013-2010) = 11/3

The second student Tracy has used the no of years from 2010 i.e.(0,,48) and (3,59)

For Tracy slope = change in y/change inx = (59-48)/(3-0) = 11/3

We find the the slopes are the same.

Y intercept for Tracy would be 48 but definitely Melaine would not have 48 as y intercept.

Hence these two lines the two students get would be one the transformation of other by shift horizontally 2010 units to left.

Thus slope is the same but intercept differs.