Answer:
1.)
A.) The graph does represent a proportional relationship because if you calculate the slope, it's 2/3, which is consistent throughout the line and with the given points.
Slope calculation:
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{6-4}{9-6} \\\\\frac{2}{3}[/tex]
B.) The coordinate (0,0) represents that no laps have been completed nor has the time started
C.) The coordinate I chose is (6,4). It represents that 4 laps were completed in 6 minutes
2.) The values to represent a proportional relationship because once calculating the slope, which is 13, you can try it with other points. Even though there's some values missing between (6,78) and (10,130), the slope remains the same.
Slope Calculation:
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{130-39}{10-3} \\\\\frac{91}{7} \\\\\frac{13}{1}[/tex]
3.)
A.) The constant of proportionality is 7/4 or 1.75
B.) y = 7/4x
4.) She'll run 8 miles because since 3/4 of an hour equates to 6 miles and there's 1/4 missing, 2 miles is 1/3 of 6 miles and 1/4 is 1/3 of 3/4 , so 1/4+1/4+1/4 = 3/4. She can run 8 miles (4*2) in 1 hour (4*1/4 hour)
