Georges asked five of his friends how long they studied for the last math test and what grade they received. he found a linear regression equation for the data to be y = 9.6x + 65.8. what does the 9.6 mean in the context of this equation?

a)his friends on average studied 9.6 hours.

b)if they studied 9.6 hours they would get a 0 on the test.

c)they should study 9.6 hours in order to get an a on the test.

d)for every hour they studied their grade would go up 9.6 points.

D

Step-by-step explanation:

65.8 in this equation would be the base grade if they studied for no period of time. 9.6 in this context would show how much their grade would go up by depending on (x) amount of hours.

As an example;

0 hours studied: 9.6(0) + 65.8 = 65.8

1 hours studied: 9.6(1) + 65.8 = 75.4

2 hours studied: 9.6(2) + 65.8 = 85

..and so on

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .