Use the graph below to answer the following question.
Find the slope of the line. Describe how one variable changes in relation to the other.
A coordinate graph is titled Distance Traveled. The horizontal axis is titled Time in hours. The vertical axis is titled Distance in miles.
The line starts at the origin and passes through the point with coordinates 1 comma 2, the point with coordinates 2 comma 4, the point with coordinates 3 comma 6, and the point with coordinates 4 comma 8.
A. 2; distance increases by 2 miles per hour
B. 2; distance decreases by 2 miles per hour
C. one-half; distance increases 1 mile every 2 hours
D. one-half; distance decreases 1 mile every 2 hours
The correct answer is A. The slope of the line is 2, which means that for every one unit increase in time, there is a two unit increase in distance. Therefore, the distance increases by 2 miles per hour.
To find the slope of the line, we can use the formula:
slope = (change in vertical distance) / (change in horizontal distance)
Looking at the graph, we can see that as the time increases by 1 hour, the distance traveled increases by 2 miles. This is true for each point on the line.
So, let's calculate the slope using two points on the line. Let's take the points (1, 2) and (2, 4).
The change in vertical distance (distance) is 4 - 2 = 2 miles.
The change in horizontal distance (time) is 2 - 1 = 1 hour.
Therefore, the slope of the line is:
slope = 2 miles / 1 hour = 2
This means that for every 1 hour increase in time, the distance traveled increases by 2 miles.
So, the correct answer is:
A. 2; distance increases by 2 miles per hour
To find the slope of the line, we can use the formula:
slope = (change in distance) / (change in time)
Looking at the graph, we can observe that for every increase of 1 in the horizontal axis (time in hours), there is a corresponding increase of 2 in the vertical axis (distance in miles).
Since the change in distance is 2 for every change in time of 1, the slope of the line is 2.
Therefore, the correct answer is A. 2; distance increases by 2 miles per hour.