Question

Consider the following graphs.

Determine the rate of change shown in each graph and determine if each is positive or negative.

Restate the rate of change as a unit rate for each graph. Explain its meaning.

Tell whether the graphs represent proportional relationships. Explain your reasoning

Answer 1

See explanation

Explanation:

Graph A:

This graph passes through the points (1,220) and (7,40). Determine the rate of change:

`(40-220)/(7-1)=(-180)/(6)=-30`

This rate of change is negative. The meaning of this rate of change is

Each second the elevation decreases by 30 feet.

This is not proportional relationship, because this graph does not pass through the origin.

Graph B:

This graph passes through the points (0,0) and (8,20). Determine the rate of change:

`(20-0)/(8-0)=(20)/(8)=2.5`

This rate of change is positive. The meaning of this rate of change is

Each loaf needs 2.5 cups of flour.

This is proportional relationship, because this graph passes through the origin and is a straight line.