Interpret Graph of a Situation

How can you identify a proportional situation in a graph?

• The graph will show a straight line passing through the origin.

• The graph will show a curved line passing through the origin.

Answer explanation

In a proportional situation, the graph will always show a straight line passing through the origin. This is because the ratio between the two variables remains constant throughout, which is represented by a straight line. The other option of a curved line is incorrect as it represents a non-proportional relationship.

In a proportional situation, what does the slope of the graph represent?

• Y-intercept

• Rate of change or constant of proportionality

Answer explanation

In a proportional situation, the slope of the graph represents the rate of change or the constant of proportionality. This means that for every unit increase in the x-axis, the y-axis increases by a constant amount. This constant amount is the slope of the graph, which is the rate of change or constant of proportionality in this context.

What does it mean for a graph to have a varied scale?

• The intervals or units on the graph's axes are not consistent or equal.

• The graph has multiple axes.

Answer explanation

A graph with a varied scale means that the intervals or units on the graph's axes are not consistent or equal. This is the correct answer because it directly addresses the question about what it means for a graph to have a varied scale. The other option, which suggests that the graph has multiple axes, does not necessarily imply a varied scale.

Match the following This graph shows the population of mice in a study, modeled as a function of time. The study begins on day 0 and ends on day 200. Select True or False for each statement.

• False

• There are two intervals of time where the mouse population decreases.

• True

• The mouse population was decreased between day 40 and day 80.

• True

• The least number of mice during the study was 130.

• True

• The mouse population was the greatest around day 160.

A bird flies out of its nest.  This graph represents the distance it flies from its nest (in meters) as a function of time (in seconds).

Place a X to mark the point on the graph that represents the bird’s greatest distance from its nest.

Place a O to mark the point that represents the bird’s return to its nest.

a

b

X

O

Match the following This graph shows the population of mice in a study, modeled as a function of time. The study begins on day 0 and ends on day 200. Select True or False for each statement.

• True

• The mouse population was the greatest around day 160.

• False

• There are two intervals of time where the mouse population decreases.

• True

• The mouse population was decreased between day 40 and day 80.

• True

• The least number of mice during the study was 130.

A bird flies out of its nest.  This graph represents the distance it flies from its nest (in meters) as a function of time (in seconds).

Place a X to mark the point on the graph that represents the bird’s greatest distance from its nest.

Place a O to mark the point that represents the bird’s return to its nest.

a

b

X

O

This graph represents (a)   .

• Constant Speed

• Acceleration

• Not moving

Identify the following two points on the graph. (1) The bird's greatest distance from its nest. (2) The point that represents the bird's return to its nest.

a

b

(1)

(2)

Explain how to interpret a graph with a varied scale.

• Carefully analyze the axes, units, tick marks, and annotations to understand the scale and interpret the data accurately.

• Use the same scale for all variables on the graph.