Question

Donald's Earnings, x (dollars) Fallons Earnings, y 38 45 43 50 48 55 53 60 58 65 Which equation best represents Fallon's earnings in terms of Donald's earnings? A. y=x+7 B. X=7y C. y=7x D. x=y+7

Answer 1

Given:

The table of values for Fallon's earnings in terms of Donald's earnings.

To find:

The equation that best represents Fallon's earnings in terms of Donald's earnings.

Solution:

In the given table the x-values are increasing by 5 units and y values increasing by 5 units. It means the rate of change of y with respect to x is constant and the table represents a linear function.

If the graph of a linear function passes through two points, then the equation of linear function is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Consider any two points from the table. Let the two points are (38,45) and (43, 50). Then, the equation is

`y-45=(50-45)/(43-38)(x-38)`

`y-45=(5)/(5)(x-38)`

`y-45=1(x-38)`

`y-45=x-38`

Adding 45 on both sides, we get

`y=x-38+45`

`y=x+7`

Therefore, the correct option is A.