How to find slope in this context.

Question

_{George is loading freights in an evator. The weight limit is 1000 pounds. He weighs 210. He has loaded 15 boxes. Each box weighs 50 pounds. Identify the slope in this situation}

Answer 1

First, let’s determine the independent variable (the one that is free to change) and the dependent variable (the one that changes whenever the independent variable changes).  We usually name the independent variable x and the dependent variable y.

The weight of the cargo varies as the number of boxes loaded varies.  Note that the other weights are constants (but maybe George would like his weight to vary a little). So the weight of the cargo in the elevator, so far, is:

      y = 50(15) + 210

 

There is a weight limit of 1000.  That means that y <=1000.  Now, to show this on a graph, the line y=50x + 210  is used (the allowable points, which are determined by natural number values of x, are on this line).  The slope of the line is 50  (remember that y=mx + b has m as the slope).   Also, the slope indicates the "rise over run," that is, the increase in the y value for each increase of 1 in the x value.  In this formula, that is 50 pounds for each additional box.

 

But, the horizontal line y = 1000 also sets an upper limit (the weight limit), but most people would allow exactly 1000 pounds on the elevator The acceptable values must be below the y=1000 line and natural numbers for x on the other line.   

Answer 2

Hi George,

 

Let's begin by writing the slope-intercept form of an equation describing a linear relationship:

    y = mx + b (where m is the slope and b is the

y-intercept)

 

Now let's plug in our values from the context of our problem and see what our equation looks like:

    y = maximum weight (1000 lbs.)

    m = constant weight per box (50 lbs.)

    x = number of boxes (15)

    b = initial weight, i.e. George's weight (210 lbs.)

    1000 = 50(15) + 210

 

Now let's see if both sides match:

    1000 = 750 + 210

    1000 = 960

 

Looks like right side is 40 lbs. short - if we add another box (50 lbs.), we'll exceed the maximum weight of 1000 lbs. by 10 lbs.

 

So looks like we have a 15 box limit (maximum value of x). and our slope in this context is the constant weight per box (50 lbs). 

 

Thanks for submitting this problem and glad to help.

 

Regards, Jordan.