Match a Description with a Graph

A graph can be used to model a situation. You can use what you know about slope and $y$-intercept to connect the graphs to real situations.

Match each description with one of the graphs above:

1. Elena begins at home and runs away from her home at a constant rate.

Elena starts at home, so the graph must start at the origin. She moves away from home at a constant speed, so the graph must be a line that increases to the right. Graph B matches the description.

2. Clare begins her walk at school and walks home at a constant rate.

Clare starts at school, so the $y$-intercept is a point on the $y$-axis that shows the distance her home is from the school. She moves closer to home at a constant speed, so the graph must be a line that decreases to the right. Graph C matches the description.

3. Lin begins at home and runs away from home, and then walks for a while.

Lin starts at home, so the graph must start at the origin. She starts running and then walks, so the graph is a line with a slope that starts off steep and then continues with a less steep slope. Graph A matches the description.

Try it

Match a Description with a Graph

Describe the graph. You can use the wording from the previous problem as a guide.

Here is how to describe the graph:

The graph starts at the origin, so the walker starts at home. The line is increasing, so the walker is moving at a constant speed away from home. Then the line decreases at a constant rate, so the walker is moving at a constant rate toward home.

Here is a possible description:

Lin begins at home and walks away from home for a while, and then she walks back home.

Video: Slope and Intercept in Tables

Watch the following video to find the meaning of slope and intercepts in context.

Khan Academy: Slope and Intercept in Tables