Warm up 1/30

1) Which of these ratios is not a rate:60 words per minute, 12 cats to 32 dogs, $8 per hour, 35 miles per gallon2) 52% of the television audience in the U.S. watched Super Bowl XXX. Write 52% as a fraction and a decimal.3) ½ of my students are sweet!! Write ½ as a percent and a decimal.

Warm Up 2/1

Solve the following one-step inequalities and then graph them.

1)t – 5 ≤ 82)52 + y > 803)14x < 2384)q ÷ 16 ≥ 108

Direct Variation…

Where graphing and tables play a big role!

Direct variation

• A direct variation is the relation between 2 quantities whose ratio remains constant.

Therefore the will always be a constant.

X and Y

• X is the independent variable because it is the input.

• Y is the dependent variable because it is always the output value

K is the constant

• “ k represents the constant of proportionality” as x and y values change, this stay the same

• When one variable increases, the other variable increases.

K notes

• When y values are bigger than your x values then your k is a whole number

• When y values are smaller than your x values then your k is either a fraction or a decimal.

Practice using tables

y = 9x x 0 2 3 5 8

y

Practice using tables

y = 12x x 1 6 12

y 48 120

Practice using tables

y = 1.25x x 0 2 4 6 8

y

Practice using tables

y = 2/5x x 0 4 9 20

y 4

Now lets make the rule based on the table

Y= ????

What is the constant?? What is the one thing not changing… it is not the x or y!

x 0 1 2 3 4

y 0 5 10 15 20

Now lets make the rule based on the table

Y= ????

What is the constant?? What is the one thing not changing… it is not the x or y!

x 0 9 12 21 27

y 0 3 4 7 9

Maddie is purchasing tickets to a Justin Bieber concert. Tickets cost 35 a piece.

• Since tickets cost $35, that is the _______, because this won’t change!!

• X is the input (or independent variable) and this is the number of tickets purchased

• Y is the output or dependent variable and this it the _______ cost.

• Rule: y =35x

X (# tickets)

0 2 3 6

Y

Kevin is saving up for a new Tony Hawk game for his Wii. He earns $7.50 for each

chore he does. What is k, the constant?

_____________________________________

X, the input, is the number of chores Kevin completes.

Y, the output, is the amount of money Kevin makes.

What is the equation? _________________What would the table look like….

X (# chores completed)

0 2 10 15 20

Y (total money earned)

The table to show y=kx

There are 37 boys in the drama club. They want to buy new props, so they are all going to pitch in some money. They all want to pitch in the same amount.

K, the constant, is 37. This number is not going to change.

The amount that each boy brings in is the input, or the _________ value.

The total amount raised is the output, or the _____ value.

What is the equation? _____________________

NOW MAKE A TABLE

The table to show y=kx

X (amount each boy brings)

0 2 3 5 10

Y (total amount raised)

Let’s create a table and graph

Let’s create a table and graph

Let’s create a table and graph

Let’s create a table and graph

Let’s create a table and graph

Let’s create a table and graph

Let’s create a table and graph