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The function shown models the depth d

(in inches) of snow on the ground during
the first 9 hours of a snowstorm, where t
is the time (in hours) after the snowstorm
begins.
The -intercept means that there
were[ Jinch(es) of snow on the ground at
the start of the storm and the slope
means that[ Jinch(es) of snow falls every
hour during the storm.
Function: d(t)= 1/2t 6

1 Answer

2 votes

Final answer:

The y-intercept of the function is 6 inches, indicating there were 6 inches of snow on the ground at the start of the storm. The slope of the function is 1/2, signifying that snow falls at a rate of 1/2 inch per hour during the storm.

Step-by-step explanation:

The question provided relates to the function d(t) = 1/2t + 6, which models the depth of snow on the ground during a snowstorm in relation to time passed. The y-intercept of the function gives us the starting condition, which is the amount of snow on the ground when t is zero. In this case, the y-intercept is 6, meaning there were 6 inches of snow on the ground at the start of the storm. As for the slope of the function, which is 1/2, it indicates the rate of snowfall, meaning that each hour, 1/2 inch of snow falls.

To determine the slope, one could select two points on the function and use the formula for slope, which is the change in y (rise) over the change in x (run). However, since the function is given in slope-intercept form, we already have the slope directly from the equation. Nonetheless, if we use two arbitrary points (for instance, t = 0 and t = 9), we can calculate the difference in snow depth at these times and divide by the time difference to confirm the slope.

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