Question

which color line on the graph shows an object with the slowest constant speed?
orange
blue
purple

Explanation:

Step1: Recall the formula for speed

Speed \(v=\frac{d}{t}\), where \(d\) is distance and \(t\) is time. On a distance - time graph, the slope of the line represents the speed. The formula for the slope \(m\) of a line is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For a distance - time graph (\(y = d\) and \(x=t\)), the slope \(m=\frac{\Delta d}{\Delta t}\) (which is speed).

Step2: Analyze the slopes of the lines

A smaller slope means a slower speed. Looking at the distance - time graph, the purple line has the smallest slope among the three lines (orange, blue, and purple). Since the slope of the distance - time graph gives the speed, the object represented by the purple line has the slowest constant speed.

Answer:

purple