Question

The two tables below show the amount of tip, y, included on a bill charging x dollars. mc026-1.jpg mc026-2.jpg Which compares the slopes of the lines created by the tables? The slope of the line for Restaurant B is mc026-3.jpg times greater than the slope of the line for Restaurant A. The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A. The slope of the line for Restaurant B is 5 times greater than the slope of the line for Restaurant A. The slope of the line for Restaurant B is 10 times greater than the slope of the line for Restaurant A.

Answer 1

The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.

Answer 2

You did not attach the table which shows the value of x and y for Restaurant A and Restaurant B. However I have dug up on other sources and I believe the given table is:

Restaurant A

x              y

10           1

20           2

30           3

Restaurant B

x              y

25           5

50           10

75           15

 

We can calculate for the slope of the line (m), using the formula:

m = (y2 – y1) / (x2 – x1)

given that (x1, y1) and (x2, y2) are given pairs of the data set

 

Calculating the slope for Restaurant A:

mA = (2 – 1) / (20 – 10)

mA = 1 / 10

 

Calculating the slope for Restaurant B:

mB = (10 – 5) / (50 – 25)

mB = 5 / 25

mB = 1 / 5

 

Dividing mB by mA to know how much larger mB is:

mB / mA = (1 / 5) / (1 / 10) = 2

 

Therefore the slope of restaurant B is 2 times greater than that of A.

 

Answer:

The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.