b How many inches does the depth of the snow increase by and what is the depth of the snow at t=0?
A
aGraph:
Domain: 0≤ t≤ 9 Range: 6≤ d≤ 10.5
B
b See solution.
Practice makes perfect
a Let's start with determining the slope and the d-intercept of the given function to graph it.
d(t)=1/2t+6
We can notice that the given function is in slope-intercept form.
y= mx+ b
In this form, m tells us the slope and b states the yt-intercept. However, for the given equation, b stands for the d-intercept.
m=1/2 b=6
Now that we know the slope and d-intercept of the function, our first step is to plot the d-intercept and find a second point using the slope. Notice that the d-axis represents the depth and t-axis represents the time.
Next, we will draw the line that represents the function. However, we have two restrictions. Since the time cannot be negative, t will be greater than or equal to . Moreover, because the function models the first 9 hours of the storm, t will be less than or equal to 9.
Now, we are able to determine the domain and range of the function. In order to do that, we will draw vertical and horizontal lines at the endpoints of the line segment to create a rectangle view of the domain and range.
The intersection points of the vertical lines with the t-axis determine the domain.
Domain:0≤ t≤ 9
The range is determined by the points where the horizontal lines intersect the d-axis.
Range:6≤ d≤ 10.5
b Now let's interpret the slope and d-intercept.
In Part A, we found that the slope is 12. Since the function models the depth of the snow, the slope tells us the depth of the snow increases 12 inch every hour.
The slope of the function represents the depth of the snow just before the storm starts. This means that the depth of the snow is 6 inches at t=0.
