At the end of a snow storm, Tristan saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. After the storm,
the snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours
after the storm ended, the depth of snow was down to 9 inches. Write an equation for
S, in terms of t, representing the depth of snow on Tristan's lawn, in inches, t hours
after the snow stopped falling.

The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours  after the snow stopped falling is:

A linear function in the model will have the following format:

In which:

The snow melts at a rate of 0.75 inches per hour, thus and:

After 4 hours, there were 9 inches, that is, when , and this is used to find S(0).

Hence, the equation is:

A similar problem is given at link

Step-by-step explanation:

Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours  after the storm ended, after the storm ended, the depth of snow was down to 9 inches.

Snow melted in 4 hours =

Initial depth of snow = 9 + 3 inches = 12 inches.

Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)

Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.

Then,

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step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be