Question

the figure above shows the relationship between the time a student spends studying and the student’s gpa that semester. the slope of the relationship at point a equals

○ 3.

○ 3/20

○ 2/20.

○ 0.

○ 1/20.

Explanation:

Step1: Understand the slope at a point

The slope of a curve at a point is equal to the slope of the tangent line at that point. Looking at the graph, the straight line (tangent or maybe a linear relationship line) passes through (0, 2) and (20, 3) (since at point A, hours of study is 20 and GPA is 3, and the other line starts at (0, 2)).

Step2: Calculate the slope

The formula for slope is $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in y (GPA) and $\Delta x$ is the change in x (hours of study). Here, $\Delta y = 3 - 2 = 1$? Wait, no, wait. Wait, the linear line: when x=0, y=2; when x=20, y=3. So $\Delta y = 3 - 2 = 1$, $\Delta x = 20 - 0 = 20$. Wait, no, maybe I misread. Wait, the curved line starts at (0,0), and the straight line starts at (0,2). At point A (20, 3), the slope of the tangent (the straight line) is $\frac{3 - 2}{20 - 0}=\frac{1}{20}$? Wait, no, wait, let's check again. Wait, the options include 1/20. Wait, the straight line: from (0,2) to (20,3). So the change in y is 3 - 2 = 1, change in x is 20 - 0 = 20. So slope is $\frac{1}{20}$. Wait, but let's confirm. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Taking two points on the tangent line: (0, 2) and (20, 3). So $m=\frac{3 - 2}{20 - 0}=\frac{1}{20}$.

Answer:

1/20 (the option with 1/20)