Part a.
We are asked to type an equation that could represent the line of best fit shown in the following image:
So, we need just two points on the line that can be used to find the slope and finally the complete equation of the line.
We select two particular points: (1, 61) and (8, 71) whcu seem to be two points where the line goes through.
Then we use the formula for the slope of a line through two points on the plane:
slope = (y2 - y1) / (x2 - x1)
in our case: (71 - 61) / (8 - 1) = 10 / 7
Then the slope-intercept form ofthe equation should look like:
y = 10/7 x + b
we can determine "b" by using one of the points (for example (1, 61)):
61 = (10/7) (1) + b
61 - (10/7) = b
b = 417/7
The final form of the equation is:
y = 10/7 x + 417/7
In approximate decimal form it becomas:
y = 1.43 x + 59.8
Part b:
Interpretation of the slope and y-intercept:
The slope represents the change in percent of graduates per year. so every year there is an increase of about 1.43 % of graduates relative to the previous year.
The y-intercept represents the graduation rate (about 59.8%) when this study started (year 0 zero corresponding to 1998)
Part c:
In order to estimate the prediction of percent of graduates in the year 2020, we first calculate the number of years between 2020 and 1998:
2020 - 1998 =
