2.2 Linear Equations Day 1

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

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

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

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

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

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!

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

White Boards

2.2 Linear Equations Day 2

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

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

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

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

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

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

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

Parallel Lines:

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

2.2 Linear Equations Day 3

Perpendicular Lines: Perpendicular slope T T

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

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

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)

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

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

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

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

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

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

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