Transcript y - FCUSD.org

Warm up 8/24
Solve each equation for y.
1. 7x + 2y = 6
2.
3. If 3x = 4y + 12, find y when x = 0.
y = –2x – 8
y = –3
4. If a line passes through (–5, 0) and (0, 2), then it passes
through all but which quadrant.
IV
Be seated before the bell rings
DESK
homework
Warm-up (in
your notes)
Agenda:
Warmup
Go over hw p.
94 & 100
Quiz – Tuesday 8/12
Tomorrow
Note 2.3 & 2.4
notes
Don’t forget test retakes
Notebook
1
Table of content
1) 1-1 Sets of Numbers /1.2
Properties of Numbers
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
1
2.3 Graph linear function/
2.4 Writing linear
functions
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 slopeintercept 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 𝟏, 𝟐, and 𝟑 have the tables shown below.
Examine each of them, make a conjecture about which
will be linear, and justify your claim.
2.3 Graph & (2.4) write linear functions
+2
A linear function has
a constant rate of
change
constant rate of change
= Slope (m)
Rise

Run
+2
+2
x
–2
0
2
4
f(x)
2
1
0
–1
–1
–1
–1
Graphing Linear Functions
3 ways to graph:
1.With y-intercept and slope
2.With a point and a slope
3.With x and y-intercepts
st
1
way
Slope-Intercept Form:
y=mx+b
Example: y=-3/4x+3
2nd Way
Point & Slope:
has a slope m and
passes through the
point (x,y)
Example: slope of
3/2 and goes
through (2,2)
3rd
way
Intercepts:
Find the intercepts
and graph.
To find y-intercept:
plug in 0 for x
To find x-intercept:
plug in 0 for y
Example: y=-x+2
y-intercept:
y=-(0)+2
x-intercept:
(0)=-x+2
y=2
2=x
Vertical Lines
Horizontal Lines
.
2.4 Writing equations
Use: y=mx+b or
y-y1= m(x-x1)b
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
___
___
___
___
____
____ ______
Slope
the same
Perpendicular Lines have
_N__
___
____
____
____
___
____
____
___ ___ ___ ___ ___ ___ ___ ___ ____ ___ _____
Slope
Negative Reciprocals
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
Are the two lines Parallel or Perpendicular?
y= m x + b
slope
Rewrite in y = mx+ b
-2x
-2x
4y = -2x +9
4
4
4
1
9
y   x
2
4
Parallel Lines
Are the two lines Parallel or Perpendicular?
y  5 x  4
x  5 y  4
-4
-4
X - 4 = -5y
-5
-5
-5
1
4
 x  y
5
5
Neither Lines
y= m x + b
slope
Rewrite in y = mx+ b
Are the two lines Parallel or Perpendicular?
y  4x  7
y= m x + b
slope
1
y   y 3
4
Perpendicular Lines
Write the equation of Parallel line in the form y= m x + b
Example 1:
Write the equation of a line that is parallel
to y = -4x
-4 + 3 that contains P(1,-2).
P(1,-2)
Step 1: Find slope and a point
Step 2: Substitute slope and the point into the
point-slope form equation.
y  y1  m( x  x1 )
y  ___
-2  ___(
-4 x  ___)
1
Step 3: Rewrite in y = mx + b form.
Perpendicular Lines in the form y= m x + b
Example 1:
Write the equation of a line that is
3 -5 that contains
perpendicular to to y = -3x
P(-3,7)
P(-3,7).
Steps1: Find slope and a point
1
m=
Steps2: Substitute slope and the point into the
point-slope form equation.
y  y1  m( x  x1 )
y  ___
 ___(
1/3 x  ___)
7
-3
Steps3: Rewrite in y = mx + b form.
You try! Example
Write the equation of the line in slope-intercept form.
parallel to y = 5x – 3 and through (1, 4)
m=5
Parallel lines have equal slopes.
y – 4 = 5(x – 1)
Use y – y1 = m(x – x1) with (x1, y1)
= (5, 2).
y – 4 = 5x – 5
Distributive property.
y = 5x – 1
Simplify.
You try
Write the equation of the line in slope-intercept form.
perpendicular
to and through (0, –2)
The slope of the given line is
, so the slope of
the perpendicular, line is the opposite reciprocal
Use y – y1 = m(x – x1).
y + 2 is equivalent to y
– (–2).
Distributive property.
Simplify.
.
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.