What is the equation of the line (the line starting at (0,10) and the line ending at (15,95)) for the line of best fit in the form of? (Identify two points on your line and show how to find the slope.)
Then, using your equation that you just made what is the least number of questions that a student would need to answer correctly on the practice to earn at least a 75% on the test? How many questions are there that they need to get correct to get a 75 percent?
To find the equation of the line of best fit, we first need to find the slope of the line. The two points given are (0,10) and (15,95).
Slope (m) = (y2 - y1) / (x2 - x1)
m = (95 - 10) / (15 - 0)
m = 85 / 15
m = 5.67
Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
y - 10 = 5.67(x - 0)
y - 10 = 5.67x
y = 5.67x + 10
To find the least number of questions the student would need to answer correctly on the practice to earn at least a 75% on the test, we first need to determine the total number of questions. Let's say there are n total questions.
75% of n = 0.75n
Now, we can set up an equation using the equation of the line we found earlier:
0.75n = 5.67n + 10
Solving for n:
0.75n - 5.67n = 10
-4.92n = 10
n = 10 / -4.92
n ≈ -2.04
Since we cannot have a negative number of questions, we can conclude that the student would need to answer at least 3 questions correctly on the practice to earn at least a 75% on the test.