Understanding Proportional Relationships


Introduction to Distance Time Graph

(A). A ladybug and ant move at constant speeds. The diagrams with tick marks show their positions at different times. Each tick mark represents 1 centimeter. On the graph, lines u and v also show the positions of the two bugs.

(1). How long does it take ladybug to travel 12 cm?

(2). How long does it take the ant to travel 12 cm?

(B). In the applet below, mark and label the point on line u and the point on line v that represent the time and position of each bug after traveling 1 cm.

(1). How fast is each bug traveling?

(2). Will there ever be a time when the ant is twice as far away from the start as the ladybug? Explain your reasoning.

(3). Plot this bug’s positions on the coordinate axes with lines u and v, and connect them with a line.

(4). Write an equation for each of the three lines.


Draw a Linear Graph by Comparison.

Priya jogs at a constant speed. The relationship between her distance and time is shown on the graph. Diego bikes at a constant speed twice as fast as Priya. Sketch a graph showing the relationship between Diego’s distance and time.


Sketch the Graph of a Linear Relation.


A you-pick blueberry farm offers 6 lbs of blueberries for $16.50. Sketch a graph of the relationship between cost and pounds of blueberries.


A line contains the points (-4,1) and (4,6). Decide whether or not each of the following points is also on the line:


The points (2, -4), (x, y), A, and B all lie on the line in the applet below. Find an equation relating x and y.