"the table and the graph below each show a different relationship between the same two variables, x and y:
how much more would the value of y be on the graph than its value in the table when x = 12?
a.) 150
b.) 300
c.) 450
d.) 600"

Option (b) is correct.

The value value of y will be 300 more on the graph than its value in the table when x = 12

Step-by-step explanation:

 Given : a linear graph of given data.

We have to find the value of y when x = 12 .

We find the equation of line for the given graph.

According to table given:

A linear equation is represented as y = mx+c , where m is slope and c  is y- intercept.    

Slope is given as ,

Given : y = 120 when x = 4 that is (4,120)

and  y = 150 when x = 5 that is (5,150)

Substitute, we get,

Thus, slope is 30

Then equation becomes y = 30x + c

and to find c that is y- intercept

Put (5,150) in the above equation , we have,

⇒ 150 = 30× 5 + c

⇒ c = 0

Thus, equation will be y = 30x

To find value of y when x = 12

Put x = 12 in above , we get,

y =  30× 12 = 360      

According to graph

The equation passes to origin  thus, y intercept is 0.

and points are (2, 110)

y= mx

⇒ 110 = 2m

⇒ m = 55

Thus, equation will be y = 55x

Thus, by graph the value  y when x = 12 is

y =  55 × 12 = 660    

Thus, difference is 660 - 360 = 300  

Thus, the value value of y will be 300 more on the graph than its value in the table when x = 12

the answer to the expression is 83