Linear Equations Linear Equations FoldableFoldable

Linear Equations Linear Equations FoldableFoldableCarlos BarronCarlos Barron

Revised by Jamie Kujawa (2007)Revised by Jamie Kujawa (2007)Nkosi Poole (2012)Nkosi Poole (2012)

Materials

• Construction Paper (soft colors)• Scissors• Markers (2 Dark colors)• Pen or Pencil

Directions• Lay your construction horizontally so that

we are folding the 17 inches in half.– We want the largest viewing area as possible.

• Fold your construction paper in half, vertically down the middle (taco style).

• Fold both ends of the construction paper inward so that they meet at the center crease.

• Using a ruler, measure approximately one and a half inches from the top and mark it.

• Do the same for the other side.• Cut off the piece from both sides. Do not cut too much.

– This will be front of your foldable; your heading will be displayed here.

Heading

• Using one of your markers, write “Linear Equations” in the top as your heading.

• Measure about 5 inches from the top and mark both sides of the front cover.

• Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY.– The foldable should start taking form.

Linear Equations

Sections• Close the flaps so that you can see the front of

your cover; you should see 4 individual parts.• Using a marker, label each part as follows:

»Graphing (to graph a linear equation)»Graphically (write equation given a Graph or

2 points)»Point and Slope (Graph & write an equation

given Point & slope)»x & y intercepts (To graph and write

equations)

Linear Equations

Graphing

X & Y intercepts

Graphically

Pt & slp

THIS IS HOW YOUR FOLDABLE WILL LOOK WHEN IT IS COMPLETED

Linear Functions

Steps for Graphing

Steps for an equation from a Graph or 2 pts

Steps for an equation given slope & point

Steps for finding x & y-intercepts of an equation

Example

with graph

Example with graph

Example with graph

Example with graph

Graphing

On the inside behind the title “Graphing,” we will write the steps necessary to graph a line.

We need a slope (m). We need a y-intercept (b).

Write down the slope-intercept formula and identify its two parts.

To graph we need:• a slope (m)•A y-intercept (b)

Slope-intercept formula

Y = mx + b

Example

• On the inside of the foldable, glue the coordinate plane given to you.

• We will be graphing . - write the equation above the graph

• Identify your slope (m) and y-intercept (b).

- put a dot for the y-intercept- from the dot count up 2 and

right 3 put a dot (repeat)

- draw a line through the dots

13

2 xy

Your graph should look like this

4 y

x

7

6

5

4

3

2

1

1

6 5 4 3 2 1 7654321

2

4

3

5

6

13

2 xy

Graphically

On the inside behind the title “Graphically,” we will write the steps necessary to write an equation to a line.

We need a slope (m). We need a y-intercept (b).

Write down the slope formula.

Write the slope-intercept formula

To write the equation we need:• a slope (m)•A y-intercept (b)

Slope-intercept formula

Y = mx + b

m = y2 – y1

x2 – x1

Example• On the inside of the foldable, glue the

coordinate plane given to you.

• Plot the points and draw the line.

• Identify your slope (m) – use the formula and y-intercept (b) from the graph.

m = -3 – 0 m = -¾ b = -3 0 – -4 • Write the equation to the line given the slope

and a y-intercept. Y =-¾ x - 3

0,43,0 and

Your graph should look like thisy

x

7

6

5

4

3

2

1

1

6 5 4 3 2 1 7654321

2

4

3

5

6

Y =-¾ x - 3

Point and Slope On the inside behind the title “Point and Slope,” we will write the steps To graph: start with the point, count up and over for the slope.

To write an equation to a line. We need a slope (m). We need a y-intercept (b).

You have to find b – you are given m = x = y = so substitute in the slope-intercept form and solve to find b.

Write your answer in slope-intercept form.

To graph we need:• the point • the slope (m)

To write the equation we need:• slope (m)• y-intercept (b)

Example• On the inside of the foldable, copy:

Find a linear equation that has a slope of -3 and passes through the point (2,1).

• Graph the line• Find the equation

• Plug in the values to find b 1 = -3 * 2 + b 1 = -6 + b 1 + 6 = b

• Write the equation y = -3x + 7

1

2

3

y

x

m

bmxy

Your graph should look like this

y

x

7

6

5

4

3

2

1

1

6 5 4 3 2 1 7654321

2

4

3

5

6

y = -3x + 7

X and Y intercepts

On the inside behind the title “x & y intercepts,” we will graph two intercepts.

To find the x-intercept given the equation

To find the y – intercept given the equation

To graph: put a dot on the x intercept and a dot on the y intercept then draw a line through the points

Let y = 0 and solve for x

Let x = 0 and solve for y

Example• On the inside of the foldable:

Glue the graph and write the equation 3x-2y=6 above the graph

• Draw a dashed line ( ) under the graph • Write the equation 3x - 2y = 6 Let y = 0 and solve

• Draw a dashed line ( ) under the x intercept• Write the equation 3x – 2y = 6 Let x = 0 and solve

3x – 2(0) = 6

3x - 0 = 6

x = 6/3

So the x-intercept is

(2, 0)

3(0) -2y = 6

0 - 2y = 6

Y = 6/-2

So the y-intercept is

(0, -3)

Your graph should look like this

y

x

7

6

5

4

3

2

1

1

6 5 4 3 2 1 7654321

2

4

3

5

6

3x - 2y = 6

Special LinesOn the back side of your construction

paper, we will address horizontal lines and vertical lines.– On the top, write “Special Lines” as your

heading.– Recall that your construction paper is

folded vertically down the middle. Label the left hand side as “Vertical” and the right hand side as “Horizontal.” Special Lines

Vertical Horizontal

Vertical LinesOn the left hand side of the foldable, draw

the line x = 2.• Do we have both variables? Will it cross both axes?• Discuss points on the line {(2,-2),(2,-1),(2,0)…}• Find the slope. What is the y-intercept? Are there any

connections between the slope, y-intercept or the graph?

Horizontal LinesOn the right hand side of the foldable.

Draw the line y=3. • Do we have both variables? Will it cross both axes?• Discuss points on the line {(-4,3),(-2,3),(0,3)…}• Find the slope. Find the y-intercept.

• Under the vertical and Horizontal lines draw a dashed line

• Write PARALLEL on the left and PERPENDICULAR on the right

Special Lines

Special LinesVertical Horizontal

Parallel

Perpendicular

Parallel linesHave the same slopeFind the line parallel to y = 2x - 4 through the

point (3, -1) You have the slope (2) you need the new y- intercept.

Use m = 2, x = 3, y = -1 and y = mx + b to find the new b

Perpendicular linesSlope is opposite the reciprocalFind the line perpendicular to y = 2x - 4 thru

the point (3, -1) You have the slope (-1/2 ) you need the new y- intercept.

Use m = -1/2, x = 3, y = -1 and

y = mx + b to find the new b

Now you have a good study guide. You will have a quiz on Tomorrow, you need to

know all all all of this information to do well.

Thank You.