Question

Dorrian graphed the distance, y, traveled by 2 bikes in x seconds.

Bikes

A graph has seconds on the x-axis and distance (feet) on the y-axis. A line for bike 1 goes through points (2, 3) and (4, 6). A line for bike 2 goes through points (4, 5) and (8, 10).

If the two bikes are racing a distance of 100 feet, which bike will win the race?
Bike 2 will win because the slope of the line for Bike 2 is Five-fourths, which is greater than the slope of the line for Bike 1.
Bike 2 will win because the slope of the line for Bike 2 is Four-fifths, which is greater than the slope of the line for Bike 1.
Bike 1 will win because the slope of the line for Bike 1 is Two-thirds, which is greater than the slope of the line for Bike 2.
Bike 1 will win because the slope of the line for Bike 1 is Three-halves, which is greater than the slope of the line for Bike 2.

Answer 1

To determine which bike will win the race based on the graphs provided, we need to calculate the slopes of the lines representing the distance traveled by each bike.

**Slope Formula:**
The slope (m) of a line is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### For Bike 1:
The line for bike 1 goes through the points (2, 3) and (4, 6).

Using the slope formula:
\[ m_{Bike 1} = \frac{6 - 3}{4 - 2} = \frac{3}{2} \]

### For Bike 2:
The line for bike 2 goes through the points (4, 5) and (8, 10).

Using the slope formula:
\[ m_{Bike 2} = \frac{10 - 5}{8 - 4} = \frac{5}{4} \]

### Comparison of Slopes:
- Bike 1 has a slope of \( \frac{3}{2} = 1.5 \)
- Bike 2 has a slope of \( \frac{5}{4} = 1.25 \)

Since the slope of Bike 1 is greater than the slope of Bike 2, Bike 1 travels faster.

### Conclusion:
**Bike 1 will win because the slope of the line for Bike 1 is Three-halves, which is greater than the slope of the line for Bike 2.**