At the hardware store, a pound of 3-inch nails costs $1.75. Carol wants to graph the relationship between number of pounds and total cost. What should be the slope of Carol's graph and why?

Let x = pounds of nails (the independent variable)

Let y = the cost of x pounds of nails (the dependent variable).

When x (the pounds of nails) is varied, the cost varies proportionally.

Because the pounds of nails is the controlled variable, it is the independent variable.

Because the cost of nails depends on the pounds of nails, the cost is the dependent variable.

We can write the equation as

y = 1.75x

This equation is of the form

y = mx + c

where

m = the slope

c = the y-intercept.

Therefore the slope for our equation is 1.75.

The graph is shown below.

Note that when x=1, y=1.75.

Answer: The slope is 1.75

The equation of the line in slope-intercept form is generally expressed as,

y = mx + b

where m is the slope and b is the y-intercept.

In this item, we are given that the each pound of 3-inch nails costs $1.75. That being said, it can be deduced that an additional pound of nail will add $1.75 to the total cost of the purchase. Example, if the initial cost is $100 then, an addition of one pound of nail will make the total cost would become $101.75.

If the relationship between the number of pounds and total cost is to be graphed then, the slope will be 1.75 for the reason that is already stated above.