Question
Looking at the graph, answer the following questions:
1) Write an equation for the line of best fit
y = 25x + 40
2) Make a prediction for a student who studies 6 hours on what their math grade will be
90%
3) Make a prediction of how many hours a student would need to study for a grade of 40%
0
4) Is there a positive or negative relationship between hours studied and math grade?
There is a positive relationship between hours studied and math grade.
Step 1: Evaluating the equation for the line of best fit
The equation for the line of best fit is given as:
y = 25x + 40
Step 2: Predicting the math grade for a student who studies 6 hours
By substituting x = 6 into the equation:
y = 25(6) + 40
y = 150 + 40
y = 190
Therefore, the prediction for a student who studies 6 hours is a math grade of 190%.
Step 3: Predicting the number of hours a student needs to study for a grade of 40%
By substituting y = 40 into the equation:
40 = 25x + 40
Subtracting 40 from both sides:
0 = 25x
Dividing both sides by 25:
0/25 = x
x = 0
Therefore, the prediction for the number of hours a student needs to study for a grade of 40% is 0 hours.
Explanation:
To determine the equation for the line of best fit on a graph, you can use linear regression analysis. This statistical technique analyzes the relationship between two variables and finds the best fitting line that represents that relationship. The equation of the line of best fit is in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To calculate the slope (m) of the line of best fit, you need to find the change in y divided by the change in x between any two points on the line. In this case, we will choose two points, (0,40) and (1,65), from the graph.
The change in y = 65 - 40 = 25
The change in x = 1 - 0 = 1
So, the slope (m) = 25/1 = 25.
Next, we need to find the y-intercept (b) of the line of best fit. The y-intercept is the value of y when x is zero. From the graph, we can see that when x is zero, the value of y is 40.
So, the y-intercept (b) = 40.
Therefore, the equation for the line of best fit is y = 25x + 40.
Now, to make a prediction for a student who studies 6 hours, we substitute the value of x (6) into the equation:
y = 25(6) + 40
y = 150 + 40
y = 190
So, the predicted math grade for a student who studies 6 hours is 190%.
Finally, to predict the number of hours a student would need to study for a grade of 40%, we can set y = 40 in the equation and solve for x:
40 = 25x + 40
-25x = 40 - 40
-25x = 0
x = 0
Therefore, for a student to achieve a grade of 40%, they would need to study 0 hours.
Please note that these predictions are based on the assumption that the data follows a linear relationship, and there may be other factors influencing the grades that are not accounted for in this analysis.