Question

Relationship A has a greater rate than Relationship B. This table represents Relationship B.
Hours worked 2 4 5 8
Amount paid ($) 25 50 62.50 100

Which equation could represent Relationship A?

Hours worked is represented by x and Amount paid is represented by y.

Select each correct answer.

y = 13x
y = 11.5x
y = 12.75x
y = 12.25x

Answer 1

the answer is y=12.75x 

12.75(2)= 25.5
12.75(4)= 51
12.75(5)= 63.75
12.75(8)= 102

Answer 2

Answer:

y = 13x ; and y = 12.75x

Explanation:

The rate of change is another name for slope.  To find the slope of Relationship B, we use the formula

$m = \frac{y_2-y_1}{x_2-x_1}$

Using the first two points, we have

m = (50-25)/(4-2) = 25/2 = 12.5

This means that anything with a rate of change greater than 12.5 works in this problem.

The equations listed for Relationship A are in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept (in all of these, b = 0).

In the first equation, m = 13; in the second equation, m = 11.5; in the third equation, m = 12.75; and in the fourth equation, m = 12.25.  The only ones with higher slopes than Relationship B are the first and the third one.