Chose the best fit linear model for the data set graph (linear model A or linear model b)
- The best fit is linear model A, we can see that the points (1,1) and (7,8) is included in this line.
Question 3: Identify the linear model you chose (A or B), justify your
selection and write an equation in slope-intercept form for the linear
model. Explain and identify the variables that are represented by the
x-values and the y-values.
- We calculate the slope of the linear model A, because it fits the data in the table, so we need two points for it (1,1) and (7,8), then the slope m is:
m = (8 - 1)/(7 - 1)
m = 7/6
then we use the line equation for one point and slope:
y - y1 = m(x - x1)
where x1, y1 are the coordinates of a point, we use point (1,1):
y - 1 = (7/6)(x - 1)
y = (7/6)x - 7/6 + 1
y = (7/6)x - 1/6
therefore the y intercept is -1/6
The y axis represents the points gained and the x axis represents the number of study sessions attained.
Question 4: What are the slope and the y-intercept? Use this information
to describe, with specific numbers, to new students what they might
expect from attending Ms. Perez’s sessions.
- the slope and y intercept were calculated in the previous question:
m = 7/6
the y intercept is -1/6
It means that you start with -1/6 points gained, then per each session you attend, you earn 7/6 points that keep adding as you attend sessions
Question 5: Ms. Perez was unable to get in touch with Melanie, who
attended the most sessions of all of the participants in this group.
Melanie attended 8 sessions. According to the data, what is a good
prediction of the number of points Melanie gained on the test? Show your
work or explain. (Hint: Use the linear model you selected.)
- lets apply our linear equation and solve:
y = (7/6)x - 1/6
y = (7/6)(8) - 1/6
y = 56/6 - 1/6
y = 55/6
So Melanie gained 55/6 points
