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 :)