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....
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Transcript of 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....
![Page 1: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/3.jpg)
Don’t forget test retakes
![Page 4: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/6.jpg)
2.3 Graph & (2.4) write linear functions
How much do you know
Write down as many word as you can about linear functions.
____________________________________________________________________________________
![Page 7: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/7.jpg)
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.
![Page 8: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/9.jpg)
3 ways to graph:1.With y-intercept and slope2.With a point and a slope3.With x and y-intercepts
Graphing Linear Functions
![Page 10: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/10.jpg)
Slope-Intercept Form:y=mx+b
1st way
Example: y=-3/4x+3
![Page 11: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/11.jpg)
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)
![Page 12: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/12.jpg)
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
![Page 13: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/13.jpg)
Vertical Lines Horizontal Lines
.
![Page 14: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/14.jpg)
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
![Page 15: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/15.jpg)
Writing equations
![Page 16: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/16.jpg)
Find equation of line given two points (–1, 1) and (2, –5).
![Page 17: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/17.jpg)
You try!Find equation of line given two points (–2, 2) and (2, –4) in point slope form.
![Page 18: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/18.jpg)
Parallel and Perpendicular Lines
![Page 19: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/19.jpg)
Parallel Lines have
___ ___ _______ ___ ____
___ ___ ____ ______ ___ ___ ____ ______
SS ll oo pp ee
the same
![Page 20: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/20.jpg)
Perpendicular Lines have
_NN__ ___ ____ ____ ____ ___ ____ ____
___ ___ ___ ___ ___ ___ ___ ___ ____ ___ _____
Negative Reciprocals
SS ll oo pp ee
![Page 21: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/21.jpg)
Parallel and perpendicular lines
Parallel Perpendicular
Same slope Opposite reciprocal
![Page 22: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/22.jpg)
Parallel Line: Have the same slopes
Perpendicular Line: Have negative reciprocal slopes
3
4
4
3
negative reciprocal
Perpendicular Line:
Parallel Line:
![Page 23: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/23.jpg)
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
![Page 24: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/24.jpg)
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
![Page 25: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/25.jpg)
Are the two lines Parallel or Perpendicular?
y= m x + b
slopeslope
Perpendicular Lines Perpendicular Lines
13
4y y
4 7y x
![Page 26: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/26.jpg)
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:
![Page 27: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/27.jpg)
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=
![Page 28: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/28.jpg)
![Page 29: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/29.jpg)
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
![Page 30: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/30.jpg)
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)
![Page 31: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032714/56649e875503460f94b8a6f8/html5/thumbnails/31.jpg)
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.