Comparing Rates of Change

The following are rates of change for different functions.  Order the rates from steepest to least steep.

$$\left|18\right|,\left|-6\right|,\left|9\right|,\left|-32\right|,\left|\ -45\right|$$

Compare using $$>,<,\ or\ \equiv$$ .

$$\left|11\right|$$ ​ (a)   $$\left|-13\right|$$

$$\left|-26\right|$$ ​ ​ (b)   $$\left|16\right|$$

​ $$\left|-95\right|$$ (c)   $$\left|95\right|$$

Equation A: $$y=2x+3$$

Equation B: $$y=3x-3$$

Which equation has a steeper slope?

Equation A: $$y=-2x+3$$

Equation B: $$y=2x+7$$

Which equation has a steeper slope?

A biologist is scuba diving. The graph shows the biologist rising over time.

At what elevation did the biologist start going up?

A coworker of the biologist is scuba diving. The table shows the coworker's descent in elevation over time.

At what elevation did the coworker start descending?

Which line is the steepest?

Match the graphs to their rate of change.

*Hint: pay attention to direction and steepness*

Equation A: $$y=23x+15$$

Equation B: $$y=13x+10$$

What is the difference between the initial values?

Equation A: $$y=6x+17$$

Equation B: $$y=14x+3$$

What is the difference between the initial values?