Question

instruction
hours spent studying\ttest grade
0\t75
0.5\t80
1\t80
1\t85
1.5\t85
1.5\t95
2\t90
3\t100
4\t90
what is the equation for the line of fit?
what does the slope represent in terms of this context?
what does the y - intercept represent in terms of this context?

Explanation:

Step1: Recall the formula for the line of best - fit

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use a graphing calculator (like Desmos as suggested) or the least - squares method. For simplicity, using a graphing calculator, we input the data points ($x$: hours spent studying, $y$: test grade).

Step2: Calculate the slope and y - intercept

After inputting the data points $(0,75),(0.5,80),(1,80),(1,85),(1.5,85),(1.5,95),(2,90),(3,100),(4,90)$ into Desmos, the line of best - fit equation is $y = 3.9x+74.6$.

Step3: Interpret the slope

The slope $m = 3.9$ represents the average increase in the test grade for each additional hour of studying. That is, on average, for every one - hour increase in the time spent studying, the test grade increases by approximately 3.9 points.

Step4: Interpret the y - intercept

The y - intercept $b = 74.6$ represents the predicted test grade when a student spends 0 hours studying. That is, if a student does not study at all, the predicted grade is about 74.6.

Answer:

Equation of the line of fit: $y = 3.9x + 74.6$
Slope interpretation: On average, the test grade increases by about 3.9 points for each additional hour of studying.
Y - intercept interpretation: The predicted test grade when a student spends 0 hours studying is about 74.6.