Question

Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.

Answer 1

one may note, you kinda missed including the related pictures.

so for every added bin, the stack grows by 4 inches. rise/run, the run is 1, the rise is 4, 4/1 = m = slope

now.... in the picture not shown hehee, the 10-gallon bins, 4 of them measure up to 29 inches high.... wait a second.. I thought the rise was only 4?

well, there are 4 bins, like in this case, so the rise should be 4*4, or 16, but there are 29 inches, that means, the slack leftover is the "initial value", or y-intercept, which should be 29 - 16, or 13.

$\bf slope=m=\cfrac{rise}{run}\implies \cfrac{4}{1}\implies 4 \\\\\\ y-intercept\implies 13 \\\\\\ y=mx+b\implies y=4x+13$