12. A staircase has steps with a riser height of 8 inches and a tread length of 10 inches. a) What is the slope of each step? b) What is the slope of the staircase?

## Step 1: Calculate the slope of each step<br />### The slope of each step is the ratio of the riser height to the tread length. This can be represented as $\frac{\text{rise}}{\text{run}}$. In this case, the rise is 8 inches and the run is 10 inches. Therefore, the slope of each step is $\frac{8}{10}$, which simplifies to $\frac{4}{5}$.<br /><br />## Step 2: Calculate the slope of the staircase<br />### The slope of the staircase is the same as the slope of each individual step. This is because the overall rise and run of the staircase are proportional to the rise and run of a single step. Therefore, the slope of the staircase is also $\frac{4}{5}$.