The following situation can be modeled by a linear function. Make an equation for the linear function and use it to answer the given question. Be sure you clearly identify the independent and dependent variables. Then briefly discuss whether a linear model is reasonable for the situation described.

A snowplow has a maximum speed of 50 miles per hour on a dry highway. Its maximum speed decreases by 0.8 miles per hour for every inch of snow on the highway. According to thismodel, at what snow depth will the plow be unable tomove?(Simplify youranswer.)

A. The independent variable is the depth of snow(d), ininches, and the dependent variable is speed(s), in miles per hour. The linear function that models this situation is s=____.

B.The independent variable is speed(s), in miles perhour, and the dependent variable is the depth of snow(d), in inches. The linear function that models this situation is d=____.

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I found an example, tried for an hr, but still do not know the step to get d=31. Please use to answer help answer the question above , if need be. thx

First, identify the independentvariable, dependentvariable, initialvalue, and the rate of change. Then use the general formula for a linearfunction, shownbelow, to make a linear model for this situation.

dependent variable=initial value+(rate of changeindependent variable)

Snow depth is the independent variable.

Since the independent variable is snowdepth, which will be represented byd, the dependent variable is the maximum speed of thesnowplow, which will be represented by s. Note that the maximum speed decreases as the snow depth increases. The rate of change in this situation is 2.1 miles per hour per inch of snow.

The initial value is the beginning value of the dependent variable. The initial value is 65 miles per hour.

Use the general formula for a linear function to make a linear model for this situation. Remember that the independent variable is snowdepth, d, the dependent variable is the maximum speed of thesnowplow, s, the rate of change is 2.1, and the initial value is 65.

dependent variable=initial value+(rate of change independent variable)

s=65(2.1d)

Therefore, the equation used to model this situation is s=65(2.1d), where s is the maximum speed of the snowplow in miles per hour and d is the snow depth in inches.

Use the linear function s=65(2.1d) to determine the snow depth at which the snowplow will be unable to move. The snowplow being unable to move means the maximumspeed, s, equals0, rounding to the nearest inch.

0=65(2.1d)

d=31

Therefore, the snow depth at which the snowplow will be unable to move is about 31 inches.

It is given that the maximum speed of the snowplow decreases by 2.1 miles per hour for every inch of snow on the highway. Inreality, it is very unlikely that the snowplow always decreases by 2.1 miles per hour for every inch of snow on the highway.

Thus, the linear model is not reasonable for the situation.