a university did a study comparing absences to grade point average, which was measured on a scale from 0 to 4.

Question

they found that absences and grade point average had a linear relationship up until a student exceeded a 50% absence rate. students who were absent from a class 5% of the time had an average GPA of 2.9. students who were absent 25% of the time had an average GPA of 1.8. which of the following relationship between GPA,g, and absence rate (in percent of classes missed),a, for student who are absent less than 50%

A) g= -.055a+2.625

B) g= -.055A+3.175

C) g= .055A+2.625

D) g= 18.18a-90.9

Answer 1

The two points to use to find the linear equation are (Absence %, GPA)=

(5, 2.9) and (25, 1.8) 

The slope is

m = (1.8-2.9) / (25-5)

m = -1.1 / 20

m = -0.055

 

g = mA+b

Substitute for m and g using the values from either point.

2.9 = (5)(-0.055) + b

2.9 = -0.275 + b

3.175 = b

 

Write the equation:

g = -0.055a + 3.175

 

You could actually answer this multiple choice question as soon as you know the slope.

Since the slope is negative, the y-intercept has to be greater than 2.9.

Going further, you can see that the slope has to be negative since the GPA is lower for a greater absence.  There is only one negative slope value and the y-intercept has to be greater than 2.9.  You don't have to do any arithmetic at all.