Answer:
A.
[tex]\begin{array}{cc}x&y\\ \\1&4.5\\2&9\\3&13.5\\4&18\end{array}[/tex]
B. [tex]y=4.5x[/tex]
C. See explanation
D. 2.911 hours
Step-by-step explanation:
Ellen is training to compete in a half marathon. She currently runs at a rate of 4.5 miles per hour.
A. Let x be the time (in hours) and y be the distance (in miles). Then
[tex]x=1\Rightarrow y=4.5\\ \\x=2\Rightarrow y=4.5\cdot 2=9\\ \\x=3\Rightarrow y=4.5\cdot 3=13.5\\ \\x=4\Rightarrow y=4.5\cdot 4=18\\ \\...[/tex]
Fill these values into the table
[tex]\begin{array}{cc}x&y\\ \\1&4.5\\2&9\\3&13.5\\4&18\end{array}[/tex]
B. The equation that represents the relationship between the time she runs and the distance she runs is
[tex]y=4.5x[/tex]
C. A direct variation describes a simple relationship between two variables . y varies directly with x if [tex]y=kx.[/tex]
Since the equation of the relationship is [tex]y=4.5x,[/tex] the equation from part B is a direct variation equation.
D. If Ellen runs 13.1 miles to complete the half marathon, then y = 13.1 miles. Find time x:
[tex]13.1=4.5x\\ \\x=\dfrac{13.1}{4.5}=\dfrac{131}{45}\approx 2.91 \ hours[/tex]
