SOLUTION: Hello I am trying to help my son. The question is..Write a function rule for the input-output Table .. We figured out that there is a difference of 20 on each side but not sure ho

Algebra ->  Functions -> SOLUTION: Hello I am trying to help my son. The question is..Write a function rule for the input-output Table .. We figured out that there is a difference of 20 on each side but not sure ho      Log On


   

Question 348162: Hello I am trying to help my son. The question is..Write a function rule for the input-output Table
.. We figured out that there is a difference of 20 on each side but not sure how to put together the function rule.
Pages to read,r Pages left to read,p
10 65
30 45
50 25
70 5

Please help us..Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One approach to solving problems like this is to first graph the x- and y-inpute on a cartesian coordinate graph, that means use regular quadrille ruled graph paper.
When you do this carefully, you will notice that you have a straight line that crosses the y-axis at y=75 and it crosses the x-axis at x = 75.
From the graph, you can determine that the slope of the line is -1 because the line leans to the left (negative slope) and the slope (rise over run) is 75/75 = 1.
From this, you can write the equation of the line (the function) in the slope-intercept form: y = mx+b. where the slope is m = -1 and the y-intercept is b = 75. The function rule is:
highlight%28y+=+-x%2B75%29 or, written as a function...
highlight%28f%28x%29+=+-x%2B75%29.
Here's what the graph should look like:
graph%28400%2C400%2C-5%2C85%2C-5%2C85%2C-x%2B75%29