Pay attention to how the dependent variable is changing. Is it increasing? Is it decreasing? Or is not changing at all?
See solution.
Practice makes perfect
Sometimes an exercise asks us to sketch a graph with a specific behavior, or maybe we just want to visualize the behavior of a relation. A good way to start is thinking about if the dependent variable is increasing or decreasing. If it is increasing, we can draw the first stroke with a slope slated upwards from left to right.
A car starts moving.
In the example above, we used a distance vs time graph to model the motion of a car. If we are told that the motion is now faster — if the dependent variable changes faster with respect to the independent variable — the next stroke would now have a steeper slope.
The car starts moving faster than before.
If the exercise tells us that the dependent variable does not change, the next stroke would be a horizontal line.
The car stops moving.
Finally, if we are asked to sketch a part of the graph where the dependent variable is decreasing, we would trace the next stroke with a slope slated downwards from left to right.
The car starts slowing down.
By following these basic ideas and paying attention to the behavior of the dependent variable we want to illustrate, we can sketch any graph that changes following a linear relation!
