1. Linear Equations Foldable
Carlos Barron
Revised by Jamie Kujawa (2007)
Nkosi Poole (2012)

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

3. 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.

4. Do the same for the other side. Cut off the piece from both sides.
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

5. Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY.
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

6. 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

7. THIS IS HOW YOUR FOLDABLE WILL LOOK WHEN IT IS COMPLETED
cut in half
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

8. 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

9. 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

10. Your graph should look like this4 y x 7 6 5 3 2 1 1 6 5 4 3 2

11. 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)
m = y2 – y1
x2 – x1
Slope-intercept formula
Y = mx + b

12. 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 – m = -¾ b = -3
0 – -4
Write the equation to the line given the slope and a y-intercept. Y =-¾ x - 3

13. Your graph should look like thisx 7 6 5 4 3 2 1 1 6 5 4 3 2
Y =-¾ x - 3

14. Point and Slope To graph we need: the point the slope (m)
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)

15. Example On the inside of the foldable, copy: Graph the line
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

16. Your graph should look like thisx 7 6 5 4 3 2 1 1 6 5 4 3 2
y = -3x + 7

17. 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

18. 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)

19. Your graph should look like thisx 7 6 5 4 3 2 1 1 6 5 4 3 2
3x - 2y = 6

20. Special Lines
On 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

21. Horizontal Lines Vertical Lines
On 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 Lines
On 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.

22. Special Lines
Under the vertical and Horizontal lines draw a dashed line
Write PARALLEL on the left and PERPENDICULAR on the right
Special Lines
Vertical
Horizontal
Parallel
Perpendicular

23. Parallel lines Have the same slope Perpendicular lines
Find 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 lines
Slope is opposite the reciprocal
Find 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

24. Now you have a good study guide
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.