The grade a student earns on a test varies directly with the amount of time the student spends studying. Suppose a student spends 6.5 hours studying and makes a grade of 84% on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t, in hours? What is the graph of your equation?
(1 point)
Responses
line graph The line starts at 0 comma 0 and passes through left-parenthesis 2 comma approximately 13 right-parenthesis and left-parenthesis 7 comma approximately 44 right-parenthesis.
line graph The line starts at 0 comma 0 and passes through left-parenthesis 3 comma approximately 18 right-parenthesis and left-parenthesis 8 comma approximately 52 right-parenthesis.
line graph The line starts at 0 comma 0 and passes through 6 comma left-parenthesis 0 point 5 right-parenthesis.
The equation that relates the grade earned on a test, g, with the amount of time spent studying, t, in hours would be: g = kt, where k is the constant of variation.
To find k, we can use the given information. The student spends 6.5 hours studying and makes a grade of 84%, which can be written as 0.84. Plugging these values into the equation, we have:
0.84 = k(6.5)
Solving for k, we get:
k = 0.84/6.5 ≈ 0.1292
Therefore, the equation that relates the grade earned on a test, g, with the amount of time spent studying, t, in hours is:
g = 0.1292t
And the graph of this equation is a line that starts at the origin (0,0) and passes through the point (2, approximately 0.26) and (7, approximately 0.90).