Question

The following chart shows the number of rows in an auditorium and the total number of seats. What equation defines the number of seats with respect to the number of rows.

a) S=20R+100
b) S=40R+120
c) S=20R+60
d)S=20R

Answer 1

Answer: c) S=20R+60

Explanation:

Linear Model

The chart supplied shows the number of rows (R) in an auditorium and the total of seats (S).

We'll find the equation that relates them. The equation of a line can be expressed in the slope-intercept form:

S = mR + b

Where m is the slope and b is the intercept.

The slope is found by:

`\displaystyle m=(S_2-S_1)/(R_2-R_1)`

We'll use two sample points (20,460) and (45,960):

`\displaystyle m=(960-460)/(45-20)=(500)/(25)`

m = 20

The value of b can be found by using one of the points, for example (20,460), and having m=20:

460 = 20*20 + b

Thus: b = 460 - 400 = 60.

The equation is:

S = 20R + 60

You can test the other points and check they belong to the same line.

Answer: c) S=20R+60