Question

Relationship A has a lesser rate than Relationship B. This table represents Relationship B.

Hours worked 2 4 5 8
Amount paid ($) 36.50 73 91.25 146
Which equation could represent Relationship A?

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

Select each correct answer.

y = 18.1x

y = 18.6x

y = 18.3x

y = 18x

Answer 1

Option A and D.

Step-by-step explanation:

If a linear function passes through two points, then the rate of change is

`m=(y_2-y_1)/(x_2-x_1)`

From the given table it is clear that the Relationship B have two ordered pairs (2,36.50) and (4,73). So, the rate of Relationship B is

`m=(73-36.50)/(4-2)`

`m=(36.50)/(2)`

`m=18.25`

The rate of relation B is 18.25.

Let hours worked is represented by x and amount paid is represented by y. So the Relationship B is defined as

`y=kx`

Where, k is the rate of relationship A.

It is given that Relationship A has a lesser rate than Relationship B.

`k<18.25`

We know that

`18.1<18.25`,
`18.6>18.25`,
`18.3>18.25` and
`18<18.25`.

The relationship A could be

`y=18.1x` and
`y=18x`

Therefore, the correct options are A and D.

Answer 2

y = 18.1x ; and y = 18x

Step-by-step explanation:

The rate of change in Relationship B can be found by using the formula for slope:

`m=(y_2-y_1)/(x_2-x_1)`

Using the first two points, we have

`m=(73-36.50)/(4-2)=(36.50)/(2)=18.25`

We know that Relationship A has a lesser rate than this. The choices given for Relationship A are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept (in this case b = 0).

The slope of the first equation is 18.1; this is less than 18.25.

The slope of the second equation is 18.6; this is greater than 18.25.

The slope of the third equation is 18.3; this is greater than 18.25.

The slope of the fourth equation is 18; this is less than 18.25.