Test Review

​constant of proportionality

​Also known as "k"

Can be used in the equation y is equal to k times x or y=kx​

​unit rate

​Second quantity is ONE of something

ex:

Miles per ONE hour

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$1.25 per ONE avocado

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​proportional relationship

​Constant ratio!

The rate of change is also constant.​

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y/x = k​ y divided by x is k

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Multiple Choice

the quantity k in a relationship described by an equation of the form y=kx

• constant of proportionality

• unit rate

• proportional relationship

• scale drawing

Multiple Choice

a rate in which the second quantity is one unit

• constant of proportionality

• unit rate

• proportional relationship

• scale drawing

Multiple Choice

a relationship between two quantities in which the rate of change or the ratio of one quantity to the other is constant

• constant of proportionality

• unit rate

• proportional relationship

• scale drawing

Remember you can use the DESMOS calculator to help you divide difficult fractions like the picture to the side.

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​Finding rates

DIVIDE!!!​

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Multiple Choice

Which ratio is equivalent to the scale 3 in. : 1 ft?

• $$\frac{\frac{1}{4}in.}{\frac{2}{3}ft.}$$  

• $$\frac{2\ in.\ }{\frac{2}{3}\ ft.}$$  

• $$\frac{4\ in.}{\frac{5}{6}\ ft.}$$  

• $$\frac{5\ in.}{6\ ft.}$$  

Multiple Choice

A news radio program has 3 commercial breaks per half-hour of programming. What is the unit rate of commercials to hours of programming?

• 6 hours of programming/2 commercials

• 6 commercials/2 hours of programming

• 1 hour of programming/ 6 commercials

• 6 commercials/ 1 hour of programming

Multiple Choice

A recipe calls for  $$2$$   cups of sugar for  $$\frac{1}{4}$$  cup of butter. What is the unit rate for sugar to butter?

• 8 cups sugar/ 1 cup butter

• 1 cup sugar/ 8 cups butter

• 4 cups sugar/ 1 cup butter

• 4 cups sugar/ $$\frac{1}{2}$$   cup butter

When you are converting rates, make sure the one you are changing is on the OPPOSITE side of the fraction.

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​Convert rates

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Multiple Choice

Jana and Jenn are training to run a race. Jana runs $$3$$   miles in  $$\frac{1}{3}$$   hour. Jenn runs $$5$$   miles in  $$\frac{3}{4}$$   hour. Who runs faster, and what is the unit rate of her speed in minutes per mile? (hint look for minutes per mile!!!)

• Jenn runs faster; $$6\ \frac{2}{3}$$  minutes/mile

• Jana runs faster; $$6\ \frac{2}{3}$$  minutes/mile

• Jenn runs faster; 0.15 miles/minute

• Jana runs faster; 0.15 miles/minute

​It can be helpful to DRAW what the word problem is describing.

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Try drawing the scale and original in the next two problems!​

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Scale Drawings

Multiple Choice

A scale drawing of a rectangular mural has the dimensions 2 inches by 3 inches. The scale is 0.5 inch to 5 feet. Find the actual dimensions of the mural.

• 0.5 in by 5 ft

• 2 inch by 3 inch

• 20 ft by 30 ft

• 1 inch by 10 feet

Multiple Choice

A real drawing of a rectangular mural has the dimensions 20 feet by 30 feet.

Find the dimensions of a scale drawing with the scale 0.25 inches : 10 feet

• 1 inch by 40 feet

• 0.5 inch by 0.75 inch

• 20 ft by 30 ft

• 0.25 inch by 10 ft

You can tell a table is proportional because you can take any y divided by x and CONSISTANTLY get the same number.

Proportional Table

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​Proportional Graphs have a straight line and go through (0,0)

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​​Proportional Graph

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To find the Constant of Proportionality take y divided by x, in this case 3 divided by 2 which is 3/2.

So the equation is y=3/2x​

Equation from Table

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​ To find the Constant of Proportionality take y divided by x, in this case 1 divided by 6 which is 1/6.

So the equation is y=1/6x​

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​​Proportional Graph

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Go to HMH Ed to continue practicing for our test on THURSDAY!​

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HMH will be GRADED so try your best!​

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​YOU'RE READY!