Writing Inverse Rules Review

Inverse Variation Breakdown (pt.1)

Let's Check in on this unit.

Be ready to take notes!

What to know for the TEST

• There are three concepts you need to know:

• 1) Create an equation from a context, table, or graph

• 2) Identify Key Features of Graphs

• 3) Solve Inverse Variation Equations (by hand, with graphs, and tables)

Create from Context

• Reading a story can get stressful, so here are tips on how to write an equation to help you solve problems

• First, find your variables. There will be one complete pair of x & y.

• Then, multiply them for your Constant of Prop. K

• Substitute that into y=K/x

Create from Table

• This is similar, but no story!

• Just remember y=k/x means k=x*y

• you can multiply ALL x&y pairs to find k and substitute it into the equation!

Create from Graph

• Find several points on the graph (look for whole number pretty points!)

• Multiply their x&y values to find K

• Sub into the equation!

Lastly: Situations with 2 variables

Remember, you're just using that if y=k/x, then k=x*y. Multiply that set of variables to find K!

Questions?

Your turn! Let's practice this concept!

Multiple Choice

Create a rule for this situation: The time it takes to complete a project varies inversely with the number of employees. With 3 people a project is completed in 7 days.

• 
  

  $y=\frac{21}{x}$

• $y=2.3\cdot x$

• $y=\frac{x}{21}$

• $y=\frac{10}{x}$

Multiple Choice

Write an equation for the situation: The time T it takes to drive between Asheville and Charlotte varies inversely with the speed driven s. If a car drives 60 mph, they make it there in 140 minutes.

•  $T=\frac{8400}{s}$  

•  $T=8400\cdot s$  

•  $T=\frac{2.333}{s}$  

•  $T=\frac{s}{2.333}$  

Multiple Choice

Write an equation for this table:

• $y=\frac{40}{x}$

• $y=\frac{x}{40}$

• $y=\frac{20}{x}$

• $y=-\frac{20}{x}$

Multiple Choice

Write a rule for the table:

• $y=\frac{18}{x}$

• $y=\frac{x}{18}$

• $y=-\frac{18}{x}$

• $y=\frac{x}{-18}$

Fill in the Blank

The time it takes for construction workers to paint a house is inversely proportional to the number of workers. It took 4 painters 9 hours to complete the project. What is the TOTAL number of hours for the project?

Multiple Choice

The amount of time it takes to drive between work and home is inversely proportional to the speed driven. If it takes 15 minutes at 45 mph, what is the constant k?

• 45*15=675

• 45*15=425

• 45/15=3

• 45+15=60

Fill in the Blank

What is the constant of proportionality k?

Multiple Choice

What is the constant of proportionality k?

• This isn't inverse variation.

• k=24

• k=12

• k=-24

Fill in the Blank

What is k? (Just type the number)

Fill in the Blank

What is the constant of proportionality k? (just type number answer)