Question

The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars.

Car 1
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100).
Car 2
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80).

Which comparison of the slopes of the two lines is accurate?
The slope of Car 1’s graph is 1 less than the slope of Car 2’s graph.
The slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.
The slope of Car 1’s graph is 5 less than the slope of Car 2’s graph.
The slope of Car 1’s graph is 10 greater than the slope of Car 2’s graph.

Answer 1

To find the slopes of the two graphs, we can use the formula for the slope of a line, which is given by:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

### For Car 1:
Points: \((2, 50)\) and \((4, 100)\)

Calculating the slope:
\[
\text{slope}_{Car 1} = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25
\]

### For Car 2:
Points: \((2, 40)\) and \((4, 80)\)

Calculating the slope:
\[
\text{slope}_{Car 2} = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20
\]

### Comparing the slopes:
- Slope of Car 1 = 25
- Slope of Car 2 = 20

Now we can find the difference in slopes:
\[
\text{slope}_{Car 1} - \text{slope}_{Car 2} = 25 - 20 = 5
\]

So, the slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.

The accurate statement is:
**The slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.**