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The grade a student makes on a test varies directly with the amount of time the student spends studying. Suppose a student spends 2.5 hours studying and makes a grade of 44% 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?

A. t = 8.8g
B. t = 17.6g
C. g = 17.6t
D. g = 0.06t​

User Marco Vos
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1 Answer

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Answer: C) g=17.6

The graph of this equation would be a straight line passing through the origin (0,0) with a slope of 17.6.

Explanation:

AI-generated answer

In this scenario, the grade earned on a test, g, is said to vary directly with the amount of time spent studying, t.

When two quantities vary directly, they are related by a constant ratio.

To find the equation that relates the grade earned on the test, g, with the amount of time spent studying, t, we can use the given information:

A student spends 2.5 hours studying and makes a grade of 44% on the test.

Let's denote the constant ratio as k.

Based on the direct variation relationship, we can set up the equation:

g = kt

Substituting the given values:

44% = k(2.5)

To convert 44% to a decimal, we divide it by 100:

0.44 = k(2.5)

Now we can solve for k by dividing both sides of the equation by 2.5:

0.44/2.5 = k

This simplifies to:

0.176 = k

Now we can substitute this value of k back into the equation:

g = 0.176t

Therefore, the equation that relates the grade earned on a test, g, with the amount of time spent studying, t, is:

g = 0.176t

Looking at the options provided, we can see that the correct equation is represented by option C:

g = 17.6t

The graph of this equation would be a straight line passing through the origin (0,0) with a slope of 17.6.

I hope this was helpful :)

User Alexander Knyazev
by
8.7k points

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