Chapter 7.4, Problem 8P

Consider ramps whose length and height are in the ratio 11 to 4. Let x be an unspecified number of feet, standing for the length of a ramp, and let y be the corresponding height of the ramp in feet. Think of x and y as varying together to make ramps of different lengths and heights, all in ratio 11 to 4.

a. Sketch a graph in a coordinate plane to show the relationship between the lengths and heights of these ramps.

b. Reason about quantities, and our definition of multiplication, and use math drawings to derive and explain equations of the form

   $y=c.x$ and $x=k.y$

where c and k are suitable constants of proportionality (find c and k).

c. Explain how to interpret the constants of proportionality c and k from part (b) in terms of your graph in part (a) in several different ways.