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

Answer:

y = 18.1x ; and y = 18x

Explanation:

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

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

Using the first two points, we have

$m=\frac{73-36.50}{4-2}=\frac{36.50}{2}=18.25$

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.

Answer 2

Answer:

Option A and D.

Step-by-step explanation:

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

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

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

$m=\dfrac{73-36.50}{4-2}$

$m=\dfrac{36.50}{2}$

$m=18.25$

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.