Question 1207855: 1. A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25-inch run.
Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform.
2. A report in the Child Trends DataBase indicated that, in 1996, 22.2% of twelfth grade students reported daily use of cigarettes. In 2006, 12.2% of twelfth grade students reported daily use of cigarettes. Write a linear equation that relates the percent y of twelfth grade students who smoke cigarettes daily to the number x of years after 1996.
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
1. A wooden access ramp is being built to reach a platform that sits 30 inches above the floor.
The ramp drops 2 inches for every 25-inch run.
Write a linear equation that relates the height y of the ramp above the floor
to the horizontal distance x from the platform.
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In this my post, I will solve part/question/problem 1, ONLY.
For explanations, see my notes after the solution.
The linear equation for this case is of the form y = ax + b.
Here "a" is the slope, which is the ratio of the rise in y to the run in x.
Notice that according to the problem's question, x is the distance from the platform.
So, physically, y = 30 inches at x = 0, and y decreases gradually to 0 (zero), as
coordinate x goes from the platform. Thus, in this case the slope in the equation is NEGATIVE.
Next, the problem says that ramp drops 2 inches for every 25 inch run.
It gives us the info to calculate the slope a =  =  = -0.08.
So, our equation has the form
y = -0.08x + b. (1)
To find "b", use the fact that at x= 0 the height is 30 inches, where the platform is sits.
So, in equation (1) put x= 0 and y= 30. You will get
0 = -0.08*0 + b,
or
30 = 0 + b,
b = 30.
So, your final equation is y = -0.08*x + 30, y in inches, x in inches. ANSWER
At this point, the problem is solved in full and all necessary explanations are provided.
Notice that I could write the final equation in one line, omitting all explanations.
It would be enough for a knowledgeable student (had he come with this question).
But I wrote explaining all details for a person who learns slowly and knows almost nothing in the subject.
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