4. Rosa watched the distance markers along the highway. She noticed that she had traveled \( 3 \mathrm{~km} \mathrm{in} 2 \mathrm{~min}, 6 \mathrm{~km} \) in 4 min , and 9 km in 6 min . Does this graph show direct variation? If so, give the constant of proportionality. How far will she have traveled in 10 min ?

1. Rosa's travel measurements are given as: - \( 3 \) km in \( 2 \) minutes, - \( 6 \) km in \( 4 \) minutes, and - \( 9 \) km in \( 6 \) minutes. 2. To determine if the graph shows direct variation, we need to check if the ratio of distance to time is constant. We calculate the rate (slope) for each measurement: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \] - For \( 3 \) km in \( 2 \) minutes: \[ \frac{3}{2} = 1.5 \, \text{km/min} \] - For \( 6 \) km in \( 4 \) minutes: \[ \frac{6}{4} = 1.5 \, \text{km/min} \] - For \( 9 \) km in \( 6 \) minutes: \[ \frac{9}{6} = 1.5 \, \text{km/min} \] 3. Since the rate is constant at \( \frac{3}{2} \, \text{km/min} \), the graph shows direct variation with the constant of proportionality \( k = \frac{3}{2} \). 4. To find the distance Rosa has traveled in \( 10 \) minutes, use the direct variation formula: \[ \text{Distance} = k \times \text{Time} \] Substitute \( k = \frac{3}{2} \) and \( \text{Time} = 10 \) minutes: \[ \text{Distance} = \frac{3}{2} \times 10 = 15 \, \text{km} \] Thus, the graph shows direct variation with a constant of proportionality \( \frac{3}{2} \), and Rosa will have traveled \( 15 \) km in \( 10 \) minutes.