Linear Equations

Linear Change is constant

1. Suppose you grow 1 ft. per year.

2. Suppose you travel 75 miles per hour.

3. Suppose the pool drains at a rate of 50 gallons per hour.

1 ft. per year

​

​Your Growth

75 miles every hour.

​

​Speed on the freeway

loses 50 gallons every hour.

​

​The Draining Pool

Multiple Choice

In all the graphs you just saw, it was a ....

• line

• parabola

• curvey thing

Multiple Choice

Linear Equations graph a ....

• parabola

• circle

• line

• snowman

Multiple Select

When writing linear equations, we care about two things:

• the growth

• The output when x=7

• the initial value

• the weather outside

​We always care about two things:

(1) The initial value and
(2) how the pattern is growing

Fill in the Blanks

For the tile pattern shown, how many tiles are being added at each figure?

Fill in the Blanks

For the tile pattern shown, how many tiles in Figure 0?

Multiple Choice

Which equation matches the tile pattern?

• $$\frac{1}{6}$$

• $$y=1x+6$$

• $$y=6x+1$$

• $$\left(6,\ 1\right)$$

​This table would match this tile pattern:

Multiple Choice

In a table, the initial value can be found where $$x=$$ ____ ?

• Where $$x=1$$

• The first entry of the table always

• Figure 100

• Where $$x=0$$

Multiple Choice

In a table, the growth can be found...

• You can't find the growth from a table

• Where $$x=0$$

• as you move along the y row/column.

• As you move along the x row/column.

Multiple Choice

For this table, what number goes in the first blank of the equation?

• -1

• 5

• 4

• 9

Multiple Choice

For this table, what number goes in the second blank of the equation?

• -1

• 5

• 4

• 9

Fill in the Blanks

Write an equation for the table shown at left.

$y=$ ___ $x+$ ___

(write the whole thing, without spaces)

Multiple Choice

Which table matches the equation

$$y=4x+5$$

Multiple Choice

The table matches a linear pattern.

What is the y-intercept? (a.k.a. The Initial Amount of tiles?)

• • 3 tiles

• 12 tiles

• 15 tiles

• 9 tiles

Sometimes a table is a little tricky...

​

Be alert!

Multiple Choice

The table matches a linear pattern.

What is the y-intercept? (a.k.a. The Initial Amount of tiles?)

• • -3

• 5

• 8

• 0

Multiple Choice

The table matches a linear pattern.

What is the growth/slope ?

Be Careful!

• • +8

• +4

• -4

• 0

If given an equation, can you locate the growth and initial amount?

​

Now let's go backward

Multiple Choice

The equation matches a tile pattern. How many tiles are being added at each figure?

• x

• y

• 5

• 3

Multiple Choice

The equation matches a tile pattern. How many tiles at Figure 0?

• x

• y

• 5

• 3

Fill in the Blanks

Write an equation for the table.