standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Task
Below is a table of diameters of different denominations of United States
Coins:
| Denomination | Diameter  |
|--------------|-----------|
|     Dime     | $17.9$ mm |
|    Nickel    | $21.2$ mm |
|   Quarter    | $24.3$ mm |
| Half Dollar  | $30.6$ mm |
If we place nickels around a central dime, as in the picture below, there is room
for five nickels with extra space but not enough room for a sixth nickel:
[IMG]
How many dimes fit around a central dime?  What about around a
central nickel, quarter, or half dollar?  Do the dimes fit snugly or is there
extra space?
How many half dollars fit around a central dime?  What about around
a central nickel, quarter, or half dollar?  Do the half dollars fit snugly or
is there extra room?
Extending the work in (a) and (b) above, for positive numbers $r$ and $s$
how many circles of radius $s$ will fit around a central circle of radius $r$?


aligns: no