Question

Mrs. Mitchell decided to grade her projects by giving each student 50 points if they turned in a project and then an additional 5 points for each part they got correct. After looking through some of the projects, she decided to give the students 7 points for each correct section. If Mrs. Mitchell wrote a function to describe the situation, what would change?
A. The slope
B. The y intercept
C. both the slope and the y intercept
D. The function will remain the same

Answer 1

A is the answer the slope

Answer 2

Answer: The correct option is (A). Slope.

Step-by-step explanation:  Given that Mrs. Mitchell decided to grade her projects by giving each student 50 points if they turned in a project and then an additional 5 points for each part they got correct.

If 'x' represents the number of correct parts that each student got, then the function 'y' which represents the total number of grades can be written as:

$y=5x+50.~~~~~~~~~~~~~~~~~~(i)$

After looking through some of the projects, she decided to give the students 7 points for each correct section. Then, the new function will be

$y=7x+50.~~~~~~~~~~~~~~~~~~~(ii)$

The slope intercept form of a linear function is given by

$y=mx+c,$ where 'm' is the slope and 'c' is the y-intercept.

Comparing equations (i) and (ii) with the slope-intercept form, we get

$\textup{Equation (i) - Slope, }m_1=5,~~\textup{y-intercept, }c_1=50,\\\\\textup{Equation (ii) - Slope, }m_2=7,~~\textup{y-intercept, }c_2=50.$

So, the slope will be changed and the y-intercept will be same, which results in the change of the function.

Thus, (A) is the correct option.