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

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




Adding 45 on both sides, we get


Therefore, the correct option is A.
Answer:
Step-by-step explanation:
<u>The slope is the ratio of difference of y- coordinates by the difference of x- coordinates:</u>
Initial:

Changed to:

As you can see the change is: from -1 to +6.
In a equation as follow:

The k is a transformation that moves up or down the graph of the function. If k is changed to a less value the graph moves down, If k is changed to a greather number the graph moves up.
In this case the graph moves up
To find the number of units the graph moves find the difference betwwen values of k:

Then, the parabola y=x²-1 is moved 7 units up when it is changed to y=x²+6
K is the right answer for the problem!