Question

1. the graph below shows the relationship between the studying time, in hours, and the grade that a student earned for two different courses, course a and course b. if a student wanted to earn a 90% in each course, about how many hours of studying, in total, would he/she have to do for both courses? a. 3 b. 6 c. 7.8 d. 9

Explanation:

Step1: Find Course A's slope/equation

Course A passes through $(0,0)$ and $(2,60)$. Slope $m_A=\frac{60-0}{2-0}=30$. Equation: $y=30x$.

Step2: Solve for Course A's study time

Set $y=90$: $90=30x \implies x=\frac{90}{30}=3$ hours.

Step3: Find Course B's slope/equation

Course B passes through $(0,0)$ and $(4,80)$. Slope $m_B=\frac{80-0}{4-0}=20$. Equation: $y=20x$.

Step4: Solve for Course B's study time

Set $y=90$: $90=20x \implies x=\frac{90}{20}=4.5$ hours.

Step5: Calculate total study time

Add the two times: $3 + 4.5 = 7.5 \approx 7.8$ hours.

Answer:

C. 7.8