The graph represents distance traveled varying directly with time.

Question

A graph shows Time (hours) on the x-axis with labels from 0 to 5, and Distance (miles) on the y-axis with labels from 0 to 200. A line on the graph starts at 0 hours, 0 miles and increases steadily through 5 hours, 200 miles.

What would be the distance traveled after 15 hours?

a) 675 miles
b) 600 miles
c) 750 miles
d) 40 miles

Answer 1

b) 600 miles

If distance traveled varies directly with time, the relationship is linear. Since the line on the graph passes through (5 hours, 200 miles), we can determine the equation of the line.

Slope of the line = (change in distance) / (change in time) = (200 - 0) / (5 - 0) = 40 miles per hour.

Using the equation of a line (y = mx + b), where m is the slope and b is the y-intercept, we have:

y = 40x + b

Plugging in the point (5 hours, 200 miles):

200 = 40(5) + b
200 = 200 + b
b = 0

Therefore, the equation of the line is y = 40x

To find the distance traveled after 15 hours:

y = 40(15)
y = 600 miles

Therefore, the distance traveled after 15 hours would be 600 miles.