Solve. Assume the exercise describes a linear relationship. When writing a linear equation, write the equation in
slope-intercept form.
-Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 781. Find a linear equation which fits this data.
A)y = 3.6225x - 503.25
B)y = -4.025x + 499.25
C)y = 4.025x + 499.25
D)y = 3.6225x + 503.25

Question

Quizplus · Accepted Answer

We can use the two given data points to find the slope of the line:

slope = (change in y) / (change in x)
      = (781-620) / (70-30)
      = 3.025

Next, we can use one of the data points and the slope to find the y-intercept of the line:

y - 620 = 3.025(x - 30)
y - 620 = 3.025x - 90.75
y = 3.025x + 529.75

Therefore, the linear equation in slope-intercept form is:

y = 3.025x + 529.75

Comparing this equation to the given answer choices, we can see that the best choice is C, which matches the equation we found. Let x be the number of hours of review course and y be the exam score.

We have two points: (30, 620) and (70, 781).

Using the slope formula:

slope = (change in y)/(change in x) = (781-620)/(70-30) = 3.025

Using the point-slope formula:

y - 620 = 3.025(x-30)

Simplifying:

y = 3.025x + 499.25

Therefore, the linear equation in slope-intercept form is y = 4.025x + 499.25.

Solve Assume the Exercise Describes a Linear Relationship