Warm up 8/24

Solve each equation for y.

1. 7x + 2y = 6

2.

3. If 3x = 4y + 12, find y when x = 0.

4. If a line passes through (–5, 0) and (0, 2), then it passes through all but which quadrant.

y = –2x – 8

y = –3

IV

Be seated before the bell rings

DESK

homeworkWarm-up (in your notes)

Quiz – Tuesday 8/12Tomorrow

Agenda:

WarmupGo over hw p. 94 & 100

Note 2.3 & 2.4 notes

Don’t forget test retakes

NotebookTable of content

Page1

1

1) 1-1 Sets of Numbers /1.2 Properties of Numbers

2.3 Graph linear function/

2.4 Writing linear functions

2) 1-3 Square Roots

3) 1-4 Simplify Algebra Expression

4) 1.6 Relations/1.7 functions

5) 1.9 Parent Functions

6) 2.1 Linear Equations/

2.2 Proportions

7) 2.3 & 2.4

2.3 Graph & (2.4) write linear functions

Learning targets

● 2.3: I can graph linear equations using slope and a point

● 2.3: I can graph linear equations using intercepts

● 2.3: I can graph linear equations in slope-intercept form

● 2.4: I can write the equation of a line in slope intercept form

● 2.4: I can write the equation of parallel and perpendicular lines in slope-intercept form

2.3 Graph & (2.4) write linear functions

How much do you know

Write down as many word as you can about linear functions.

____________________________________________________________________________________

2.3 Graph & (2.4) write linear functions

Functions , , and have the tables shown below. 𝟏 𝟐 𝟑Examine each of them, make a conjecture about which will be linear, and justify your claim.

2.3 Graph & (2.4) write linear functions

x –2 0 2 4

f(x) 2 1 0 –1

+2

–1

+2

–1

+2

–1

A linear function has a constant rate of change

constant rate of change

= Slope (m) Rise

Run

3 ways to graph:1.With y-intercept and slope2.With a point and a slope3.With x and y-intercepts

Graphing Linear Functions

Slope-Intercept Form:y=mx+b

1st way

Example: y=-3/4x+3

Point & Slope:has a slope m and

passes through the point (x,y)

2nd Way

Example: slope of 3/2 and goes through (2,2)

Intercepts:Find the intercepts

and graph.To find y-intercept:

plug in 0 for xTo find x-intercept:

plug in 0 for y

3rd way Example: y=-x+2

y-intercept: y=-(0)+2 y=2x-intercept: (0)=-x+2 2=x

Vertical Lines Horizontal Lines

.

Use: y=mx+b or y-y1= m(x-x1)b

2.4 Writing equations

Slope (m) Slope (m)

y-intercept Point (x1, y1)b

Writing equations

Find equation of line given two points (–1, 1) and (2, –5).

You try!Find equation of line given two points (–2, 2) and (2, –4) in point slope form.

Parallel and Perpendicular Lines

Parallel Lines have

___ ___ _______ ___ ____

___ ___ ____ ______ ___ ___ ____ ______

SS ll oo pp ee

the same

Perpendicular Lines have

_NN__ ___ ____ ____ ____ ___ ____ ____

___ ___ ___ ___ ___ ___ ___ ___ ____ ___ _____

Negative Reciprocals

SS ll oo pp ee

Parallel and perpendicular lines

Parallel Perpendicular

Same slope Opposite reciprocal

Parallel Line: Have the same slopes

Perpendicular Line: Have negative reciprocal slopes

3

4

4

3

negative reciprocal

Perpendicular Line:

Parallel Line:

Are the two lines Parallel or Perpendicular?

y= m x + b

slopeslope

Parallel Lines Parallel Lines

Rewrite in y = mx+ bRewrite in y = mx+ b

-2x -2x-2x

4y = -2x +94y = -2x +94 4 4 4 4

1 9

2 4y x

Are the two lines Parallel or Perpendicular?

y= m x + b

slopeslope

Neither Lines Neither Lines

Rewrite in y = mx+ bRewrite in y = mx+ b-4 -4-4

X - 4 = -5yX - 4 = -5y

-5 -5 -5 -5 -5

1 4

5 5x y

5 4x y 5 4y x

Are the two lines Parallel or Perpendicular?

y= m x + b

slopeslope

Perpendicular Lines Perpendicular Lines

13

4y y

4 7y x

Write the equation of Parallel line in the form y= m x + b

Example 1:

Write the equation of a line that is Write the equation of a line that is parallelparallel to y = to y = -4-4x + 3 that contains P(x + 3 that contains P(11,,-2-2).).

Step 2: Substitute slope and the point into the point-slope form equation.

Step 1: Find slope and a point

Step 3: Rewrite in y = mx + b form.

-4-4 P(P(11,,-2-2))

1 1( )y y m x x

___ ___( ___)y x -2-2 -4-4 11

Step 1:

Step 2:

Step 3:

Perpendicular Lines Perpendicular Lines in the form y= m x + b

Example 1:

Write the equation of a line that is Write the equation of a line that is perpendicularperpendicular to to y = to to y = -3-3x -5 that contains x -5 that contains

P(P(-3-3,,77).).

Steps2: Substitute slope and the point into the point-slope form equation.

Steps1: Find slope and a point

Steps3: Rewrite in y = mx + b form.

33 P(P(-3-3,,77))

1 1( )y y m x x

___ ___( ___)y x 77 1/31/3 -3-3

Steps1:

Steps2:

Steps3:

11m=m=

Write the equation of the line in slope-intercept form.

parallel to y = 5x – 3 and through (1, 4)

Parallel lines have equal slopes.

Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).

Distributive property.

Simplify.

m = 5

y – 4 = 5(x – 1)

y – 4 = 5x – 5

y = 5x – 1

You try! Example

Distributive property.

Simplify.

Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).

You try

The slope of the given line is , so the slope of

the perpendicular, line is the opposite reciprocal .

Write the equation of the line in slope-intercept form.

perpendicular to and through (0, –2)

Summarize:

In 10 words are less summarize the what you learned.

Shared with your group which concept today will most likely appear on the test.