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.)
Using your equation what is the least amount of questions that a student would need to answer correctly on the practice to earn at least a 75% on the test?
To find the equation of the line of best fit passing through the points (0,10) and (15,95), we first need to find the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
slope = (95 - 10) / (15 - 0)
slope = 85 / 15
slope = 5.67
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (0,10), we get:
y - 10 = 5.67(x - 0)
y - 10 = 5.67x
y = 5.67x + 10
Therefore, the equation of the line of best fit is y = 5.67x + 10.
To find the least amount of questions a student would need to answer correctly on the practice to earn at least a 75% on the test, we can set up the equation:
(questions answered correctly / total questions) * 100% = 75%
Let the total number of questions be x. The student must answer at least 75% of the questions correctly, so the inequality will be:
(number of questions answered correctly / x) * 100% ≥ 75%
(number of questions answered correctly / x) ≥ 0.75
number of questions answered correctly ≥ 0.75x
Since the student must answer the least amount of questions correctly to earn at least 75%, we can set the inequality equal:
number of questions answered correctly = 0.75x
Therefore, a student would need to answer at least 75% of the questions correctly on the practice to earn a score of 75% or higher on the test.