Question

at the end of a snow storm, nolan saw there was a lot of snow on his front lawn. the temperature increased and the snow began to melt at a steady rate. the depth of snow on nolans lawn, in inches, can be modeled by the equation s = -1.75t + 14, where t is the time, in hours, after the snow stopped falling. what is the y-intercept of the equation and what is its interpretation in the context of the problem?

answer attempt 1 out of 2

the y-intercept of the function is \boxed{1} which represents

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(S=- 1.75t + 14\), we can compare it with the slope - intercept form \(y=mx + b\) (here \(y = S\) and \(x=t\)).

Step2: Identify the y - intercept

By comparing \(S=-1.75t + 14\) with \(y = mx + b\), we can see that the value of \(b\) (the \(y\) - intercept) is \(14\).

Step3: Interpret the y - intercept

In the context of the problem, \(t\) is the time in hours after the snow stopped falling. When \(t = 0\) (at the time when the snow stopped falling), we substitute \(t = 0\) into the equation \(S=-1.75(0)+14=14\). So the \(y\) - intercept of \(14\) represents the depth of the snow on Nolan's lawn (in inches) at the time when the snow stopped falling (when \(t = 0\) hours).

Answer:

The \(y\) - intercept of the function is \(14\) which represents the depth of the snow on Nolan's lawn (in inches) at the time when the snow stopped falling (when \(t = 0\) hours).