Understanding Proportional Relationships

STAAR Review

Part One - Must receive a 70%

8.4(b): Proportional vs.

Non-Proportional

Relationships

Proportional relationships go

through the origin (0,0)

Proportional relationships DO NOT

have a y-intercept (b=0)

Proportional relationships are

linear

To find unit rate …

RISE (y) divided RUN (x)

Non-proportional relationships go

through the y-axis

Non-proportional relationships DO
have a y-intercept that is not zero (b)

Multiple Choice

Does this graph represent a proportional relationship?  

• No, because it doesn't pass through the origin.

• Yes, because it doesn't pass through the origin.

• Yes, because it intersects the y axis.

• No, because it intersects the x axis.

Multiple Choice

What is the unit rate?

• 10

• 5

• 1

• 2

Multiple Choice

What makes a graph proportional?

• Straight line

• The line goes through the origin

• Curvy line

• Straight line and the line goes through the origin

Multiple Choice

Ordered pair (0,0) is also known as the ___.

• y-axis

• x-axis

• origin

• constant

Multiple Choice

What does linear mean?

• Horizontal line

• Vertical line

• Curved line

• Straight line

Multiple Choice

Do proportional relationships have a y-intercept (b)?

• Yes b = 0

• No b = 0

• Sometimes, depends

Multiple Choice

A Canoe Rental company's prices are represented in the graph. What is the meaning of the point (1, 12)?

• The company charges $1 for 1 hour.

• The company charges $12 for 1 hour.

• The company charges $1 for 12 hours.

• The company charges $12 for 12 hours.

Multiple Choice

How much does it cost to have your lawn mowed for 2 hours?

• $16

• $17

• $18

• $19

Multiple Choice

Is the graph proportional or non proportional?

• Proportional

• Non proportional

Multiple Choice

Is the graph proportional?

• Proportional

• nonproportional

Multiple Choice

is the graph proportional?

• proportional

• non proportional

Multiple Choice

is the graph proportional?

• Proportional

• non proportional

Multiple Choice

Which best describes the graph represented in this table?

*Use STAT EDIT

•  proportional

• non-proportional

Multiple Choice

Is the graph proportional or non proportional?

• proportional

• non proportional

Multiple Choice

Is this table proportional or non-proportional?

*Use STAT EDIT

• Proportional

• Non-Proportional

Multiple Choice

Is this table proportional?

*Use STAT EDIT

• Yes

• No

8.4(C): Slope from Tables &

Graphs

8.5(I): Slope-Intercept

Equations

To find an equation from graph or table…

1.Find two points

2.

Stat

3.

1: Edit

4.

L1 = x values L2 = y values

5.

Stat

6.

Arrow right to calculate

7.

4: LinReg (ax+b)

8.

Enter 5x

m (a in calculator) = Slope

b = y-intercept

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2

• 3

• 5

• Cannot be Determined 

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

Multiple Choice

What is the equation of this line?

*Use STAT EDIT

• y = 2x +2

• y = 2x -2

• y = -x + 2

• Cannot be Determined

Multiple Choice

Write the equation of the line.

*Use STAT EDIT

• y = -2/3x + 4

• y = 2/3x + 4

• y = 3/2x + 4

• y = -3/2x + 4

Multiple Choice

What is the y-intercept of the line with the equation $$y\ =\ -2x\ +\ 4$$  

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

Find the slope

*Use STAT EDIT

• -5/3

• -3/5

• 5/3

• 3/5

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope

• y-intercept

• linear

• point-slope

Multiple Choice

What does 'b" represent in y=mx+b

• y-intercept

• macaroni

• nothing

• slope

Multiple Choice

Write the equation for the line.

*Use STAT EDIT

• y= -1x+3

• y= 4x+3

• y=(1/4)x+3

• y= -4x+3

8.8(C): Modeling &
Solving Equations

Example:

x

-x

-1

1

x

x

x

x

-x

-x

1

1

1

-1

-1

4x - 2

-2x + 3

​=

Multiple Select

Write an equation for the model above.

What is the equation and answer?

Select two.

• x + 3 = -9

• x - 3 = 9

• x = 6

• 3x - 1 = 9

• x =11

Multiple Select

What equation is modeled?

What is the correct answer?

Select two.

• 3 = 6

• 3x = 6

• x = 2

• 3 = 6x

Multiple Select

Which equation matches the picture above?

Key:

Cup= C

Snowflake =1

Select two.

• c = 4

• 1 + 1 = 8

• 2 = 8

• 2C = 8

Multiple Select

Using the model, write the equation and solve for x.

Select two.

• 6 = 2+x

• x = 3

• -6 = 2x;

• 6 = 2x;

• x = 9

Multiple Choice

Which equation matches the picture above?

• t = 3

• t + 4 = 7

• 1 + 4 = 7

• 4t + 1 = 7

Multiple Choice

Write the equation for the model.

• 10=2-x

• -10=-x+2

• -10=x-2

• -10=x+2

Multiple Choice

Write the equation for the model.

• -6x=-30

• 6x=-30

• 6=-30

• -6x=30

8.7(A): Volume of

Cylinders, Cones, &

Spheres

Volume of Cylinder: π r² h

Volume of Cone: ⅓π r² h

Volume of Sphere: 4/3 π r3

When given diameter, divide value BY TWO to find radius

Multiple Choice

What does a radius look like?

Multiple Choice

When given the diameter of a cylinder/cone, how do you find the radius?

• Take the square root of the diater

• Divide the diameter by 2

• Multiple the diameter by 2

• Subtract the diameter from the height

Fill in the Blank

What does big "B" stand for in the formula V = Bh

Multiple Choice

What is the formula for big B?

• π r² h

• π r²

• 1/3 π r²

• 1/3 π r² h

Multiple Choice

What is the base shape for cylinders and cones?

• Rectangle

• Square

• Circle

• Triangle

Multiple Choice

Which is the correct formula for the given problem?

• v = π 2² 5

• v = 4/3 π 2² 1

• v = π 1² 5

• v = 1/3 π 5² 1

Multiple Choice

What is the volume of this cylinder?

• F

• G

• H

• I

Multiple Choice

A cone has a height of 9 in and a diameter of 6... What is the volume of this cone?

• 84.82 in

• 339.29 in

• 254.47 in

• 1017.88 in

Multiple Select

Cylinder has a radius of 12 and a height of 9... What is the correct equation and volume of this cylinder? Use 3.14 for pi.

Select two.

• 4069.44 cm

• π 6² 9

• 1017 cm

• 3054 cm

• π 12² 9

Multiple Select

A cone has a volume of 1.5π and a height of 4.5... What is the radius of the cone?

Select two.

• 1.5π = π r² 4.5

• 1.4 in

• 1.0 in

• V = 1.5π 4.5² h

• 0.6 in

Multiple Choice

Find the volume of the given sphere.

• 418.7 cubic ft

• 3,984.6 cubic ft

• 4,188.8 cubic ft

• 4,319.8 cubic ft

Multiple Choice

Find the volume of the given sphere.

• 1,563.5 cubic in.

• 1,325.5 cubic in.

• 1,129.9 cubic in.

• 1,819.6 cubic in.

Multiple Choice

Find the volume of the sphere.

• 904.32 ft³

• 7,234.56 ft³

• 150.72 ft³