Answer
See below:
Work Step by Step
(a)
By the definition of y-intercept, the point should be on the y-axis, also x-coordinate of that point should be zero.
From the graph, it can be seen that, \[\left( 0,4571 \right)\] is the point, where x-coordinate becomes zero.
Therefore, the y-intercept is equal to 4571 units.
Also, it can be observed from the graph that, in the year of 2005, the number of deaths involving distracted driving was 4571.
(b)
By the definition of slope:
\[\begin{align}
& m=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right) \\
& =\left( \frac{5870-4571}{3-0} \right) \\
& =\left( \frac{1299}{3} \right) \\
& =433
\end{align}\]
From the graph, it can be seen that, the slope of this scatter plot represents, the change in the number of deaths per unit change of year after 2005.
Therefore, the slope is equal to 433 units. Also, the slope of this scatters plot represents, the change in the number of deaths per unit change of year after 2005.
(c)
The general equation of a line in the form of slope-intercept form is given by:
\[y=mx+c\]
From the above part (a), and (b):
\[m=433\]and,\[y-\text{intercept}=4571\]
Therefore, the equation of linear function is given by:
\[y=433x+4571\]
Hence, the equation of linear function is given by \[y=433x+4571\].
(d)
The equation of linear function is given by:
\[y=433x+4571\]
Since, in the year 2015 means: After 10 years from 2005.
So, the value of x will be 10.
Substitute the value of x with 10 in the above equation:
\[\begin{align}
& y=433\times 10+4571 \\
& =4330+4571 \\
& =8901
\end{align}\]
Therefore, in the year 2015, the number of fatalities in the United States were 8901 deaths.
