1. 2.2 Linear Equations
Day 1

2. y = mx + b y = 2x y = 1x y = 2x+ 5 Linear Equations
Mathematics is all about patterns. Certain relations would form a line on a coordinate plane (another visual to represent the data). We have a function that describes the picture, inputs and outputs… y = 2x. We can see what is happening. Let’s say this graph represents money you spend on caramel apples. How would the graph change if they cost $1 instead of $2. What if you loaned 5 dollars to your friend and then bought the $2 apples?
y = 2x+ 5
Linear Equations

3. Standard Form vs. Slope-Intercept Form
Write the following equation in standard form.
No Fractions!
Math is written in different forms all the time. Similar to fractions and decimals or Celsius and Fahrenheit, the forms mean the same thing but are written different ways.
x and y on same side!
x should be positive
Slope Intercept Form
Standard Form

4. White Boards 3∙ ∙ 3 3∙ -2x -2x Standard Form
Change from slope intercept form to standard form.
Remember, if you multiply one term you must multiply every term by the same thing…
White Boards 3∙
No fractions are allowed. You need to get rid of that 3 on the denominator. Well, that 3 is really a divide by 3, so perform the inverse. 3∙
∙ 3
In standard form x and y must be on the same side. So, move the 2x by performing the inverse, subtraction.
-2x
-2x
x should be positive. Multiply by -1 to each term. (Same as just changing the sign)
Standard Form

5. Slope is the steepness of a line
Slope is the change in the y value over the change in the x value
Slope how fast a line is rising or falling

6. Slope of Lines Slants upward (rises) left to right: Positive slope
Slants downward (falls) left to right: Negative slope
Every Vertical Line: Slope is undefined or there is no slope.
Every Horizontal Line: Slope is 0

7. Up
Down
(5, 3)
Right
Left
(0, 1)
I could use the formula… if you see a graph and you can, count… it’s easier and faster!

8. Find the slope of the line that passes through the pair of points.
(-2,1) and (6,7)

9. White Boards

10. 2.2 Linear Equations
Day 2

11. Plug in m, x, and y: solve for b Write in slope-intercept form
Writing the equation of a line.
y = mx + b
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form if directed

12. Standard Form Slope-Intercept Form SI SF 1. Slope = and
Write the equation of the line in both Slope-Intercept and Standard form.
1. Slope = and
y-intercept = -4
Always begin with slope-intercept form
Slope-Intercept Form
Standard Form
White Boards SI SF

13. SI SF 2. b = m = Slope-Intercept Form Standard Form
Write the equation of the line in both Slope-Intercept and Standard form.
Always begin with slope-intercept form 2.
b =
m =
Slope-Intercept Form SI
Standard Form
White Boards
What if the line doesn’t go through a definitive y-intercept? Well, the problem turns into type 4: writing linear equations given two points. SF

14. SF SI 3. Slope of -3 and goes through the point (-1,5)
Write the equation of the line in both Slope-Intercept and Standard form.
(x, y) 3.
Slope of -3 and goes through the point (-1,5)
Always begin with slope-intercept form
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form
Slope-Intercept Form
Standard Form SF SI

15. SI SF 4. Slope of 5 and goes through the point (9,-4) Standard Form
Write the equation of the line in both Slope-Intercept and Standard form.
White Boards
(x, y) 4.
Slope of 5 and goes through the point (9,-4)
Always begin with slope-intercept form
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form if necessary
Standard Form
Slope-Intercept Form SI SF

16. Does it matter which point you choose?
Write the equation of the line in both Slope-Intercept and Standard form. 5.
Goes through the points (-3,8) and (7,6)
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form
Slope-Intercept Form SI
Standard Form
Does it matter which point you choose? SF NO

17. 6. Goes through the points (-3,-2) and (1,6) Standard Form
Write the equation of the line in both Slope-Intercept and Standard form.
White Boards
(1/2 of the groups assigned the first ordered pair) 6.
Goes through the points (-3,-2) and (1,6)
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form
Always begin with slope-intercept form
Standard Form
Slope-Intercept Form SI SF

18. Parallel Lines:

19. 7. Standard Form Slope-Intercept Form SI SF
Write the equation of the line in both Slope-Intercept and Standard form. 7.
Write equation of the line through (5, 1) and parallel to
Find m
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form
Slope of the given line:
Slope of the parallel line:
Always begin with slope-intercept form
Standard Form
Slope-Intercept Form SI SF

20. 2.2 Linear Equations
Day 3

21. Perpendicular Lines:
Perpendicular slope T T

22. 1. Standard Form Slope-Intercept Form SI SF
Write the equation of the line in both Slope-Intercept and Standard form. 1.
Write equation of the line through (6, 1) and perpendicular to
Find m and
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form T T
Slope of the given line:
Slope of the perpendicular line: T
Always begin with slope-intercept form
Standard Form
Slope-Intercept Form SI SF

23. 2. Standard Form Slope-Intercept Form SI SF White Boards
Write the equation of the line in both Slope-Intercept and Standard form.
White Boards 2.
Write equation of the line through (2, 1) and perpendicular to
Find m and
Plug in m, x, and y: solve for b
Write in slope-intercept form
Rewrite in Standard form T T T
Always begin with slope-intercept form
Standard Form
Slope-Intercept Form SI SF

24. Begin with b Move m (more than once)
Graphing lines: Slope-Intercept Form
m = slope
b = y intercept
Begin with b
Move m
(more than once)

25. Graphing lines: Standard Formx y
0 + 3y =12
( ) y-i 4
y-intercept
2x + 0 =12
( ) x-i 6
x-intercept

26. Graph the following lines.
White Boards
Graph the following lines.

27. 0x + y = 5 x y ● ● ● 5 1 5 2 5 Horizontal Line (y=)
Graphing lines: Special Cases
0x + y = 5 x y ● ● ● 5 1 5 2 5
Horizontal Line (y=)
Goes the way of the missing letter (m = 0) 27

28. y Horizontal line = any number What does an upside-down h look like?
Is always a horizontal line.
Zero slope

29. x + 0y = 5 x y 5 5 1 ● ● 5 2 ● Vertical Line (x=)
Graphing lines: Special Cases
x + 0y = 5 x y 5 5 1 ● ● 5 2 ●
Vertical Line (x=)
Goes the way of the missing letter (m = undefined) 29

30. x Vertical line = any number
What does an upside-down and right-side up V look like?
= any number
Is always a vertical line. x
Undefined slope

31. Graph the following lines.
White Boards
Graph the following lines.