Question

the following table of values represents the cost of ordering t - shirts for company 1. determine which slope formula correctly models the relationship between the number of t - shirts ordered (x) and the total price (y). which of the following formulas correctly represents the slope between two points on the table? company 1

shirts ordered	price ($)
40	200
60	270
80	340
100	410
120	480

a ( m=\frac{200 - 130}{40 - 20}=3.5 )
b ( m=\frac{200 - 130}{340 - 270}=1 )
c ( m=\frac{200 - 40}{130 - 20}=1.45 )
d ( m=\frac{20 - 40}{130 - 200}=\frac{2}{7} )

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are table points.

Step2: Pick two valid points

Choose $(x_1,y_1)=(20,130)$ and $(x_2,y_2)=(40,200)$.

Step3: Calculate slope

$m = \frac{200 - 130}{40 - 20} = \frac{70}{20} = 3.5$

Step4: Match to options

This matches option A's calculation.

Answer:

A. $m = \frac{200 - 130}{40 - 20} = 3.5$