Question

The table shows the average bill totals for given numbers of diners at Simone’s restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?

Persons Bill Amount
1
$40
2
$80
7
$280
9
$360
11
$440
(12, 460)
(20, 800)
(24, 1,020)
(27, 1,080)
(28, 1,110)

Answer 1

(20, 800) and (27, 1080)

Explanation:

Find slope:

m = (y2 - y1) / (x2 - x1)

= 80 - 40 / 2 -1

= 40

Find b, can use any data points above. I'll just pick the first one (1, 40):

y = mx + b

40 = 40(1) + b

b = 0

Use m and b to form equation of a line:

y = mx + b

y = 40x + 0

y = 40x

Use substitution with the points in equation, if they equal then it'll lie on line.

y = 40x

Point (20, 800)

800 = 40(20)

800 = 800

Point (27, 1080)

1080 = 40(27)

1080 = 1080

The other points don't equal so they don't work.