Question

The state of Montana is experiencing a warm day after a heavy snowfall. The graph shows the height of snow, h, in centimeters after t hours.

1.) What linear function does the graph represent.

h= 3t = 6
h=3t+18
h=−3t+18
h=−3t+6
The initial value represents which of the following?

The amount of snow melting each hour.

The amount of snow remaining after four hours.

The amount of snow that accumulated the previous night.

Answer 1

1.
`h = -3t + 18`

2. The amount of snow that accumulated the previous night.

Explanation:

1. height of snow = h cm

time = t hrs

To determine the linear function, find the slope (m) of the line, and the y-intercept (b). Then represent the function in slope-intercept form as y = mx + b. Where,

y = h,

x = t

m = slope

b = y-intercept

Find slope (m) using points (6, 0) and (0, 18):

`m = (h_2 - h_1)/(t_2 - t_1) = (18 - 0)/(0 - 6) = (18)/(-6) = -3`

m = -3

The y-intercept is where the line intercepts the y-axis = 18

Substitute y = h, x = t, m = -3, and b = 18 into y = mx + b.

Thus, the linear function would be:

`h = -3t + 18`

2. The Initial value is the y-intercept, which is 18. In this case, 18 represents the amount of snow in cm, that accumulated the previous night.