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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-45=\dfrac{50-45}{43-38}(x-38)$

$y-45=\dfrac{5}{5}(x-38)$

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

$y-45=x-38$

Adding 45 on both sides, we get

$y=x-38+45$

$y=x+7$

Therefore, the correct option is A.