unit 4 - algebra1kraus / home page 4 notebook.pdfunit 1 unit 2 unit 3 unit 4 unit 5 unit 6 unit 7...
TRANSCRIPT
Unit 4 – Writing Linear Equations 1
Name: ____________________ Teacher: _____________ Per: ___
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
– Unit 4 – [Writing Linear Equations]
Find the equation of a line that has slope m = 4 and passes through the point (–1, –6).
Okay, they gave me the slope, m = 4.
Also, by giving me a point on the line, they gave me an x and a y-value: x = –1 y = –6.
In slope-intercept form (y = mx + b), I need y, m, x, and b. All I need to do is plug in what they gave me and solve for b:
y = m x + b
(–6) = (4)(–1) + b
–6 = –4 + b
+4 +4
–2 = b
For the Equation, y = mx + b, I now know both m and b so:
y = 4x – 2
Unit 4 – Writing Linear Equations 2
To be a Successful Algebra class,
TIGERs will show…
#TENACITY during our practice, have…
I attempt all practice I attempt all homework I never give up when I don’t understand
#INTEGRITY as we help others with their work, maintain a…
I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them
#GO-FOR-IT attitude, continually…
I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset
#ENCOURAGE each other to succeed as a team, and always…
I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up
#REACH-OUT and ask for help when we need it!
I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to
Unit 4 – Writing Linear Equations 3
Unit Calendar
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
Novermber 10 11 12 13 14
DLA Writing Equations
given a slope and
y-intercept
Writing Equations in
Slope Intercept Form
Writing Equations in
Point Slope Form
Converting Slope
Intercept Form
to Standard Form
17 18 19 20 21
Practice Writing
Equations
Writing equations
of Parallel and
Perpendicular Lines
Review
TEST
…
Essential Questions
How can I choose the best linear representation in this situation? And why?
Why do I translate between the various algebraic forms of a linear function?
What do the various forms they tell me?
What connections can I make between the graph and the linear equation?
How can I use linear functions to describe real world data?
How can I use linear relationships to make decisions and predictions for real world
situations?
Unit 4 – Writing Linear Equations 4
Critical Vocabulary
Slope
x-Intercept / Zero
y-intercept
Slope-Intercept Form
Point-Slope Form
Standard Form
Unit 4 – Writing Linear Equations 5
Slope-Intercept Form: Given Slope and y - intercept
Slope – Intercept Form:
Slope: y-intercept: Examples:
Write the equation of a line with a slope of 3, and y-intercept of -8. m: _______ b: ( , ) equation: __________
Find the equation of a line that crosses the y-axis at the point (0, 6) and has a rate of change of -1/3. m: _______ b: ( , ) equation: __________
Write the equation of the line graphed below.
m: _______ b: ( , ) equation: __________
Write the equation of the line represented in the table below.
x y
-4 9
-2 8
0 7
2 6
m: _______ b: ( , ) equation: __________
Unit 4 – Writing Linear Equations 6
Practice:
Write the equation of a line with a y-intercept of -3, and a slope of 1/4. m: _______ b: ( , ) equation: __________
Find the equation of a line that crosses the y-axis at the point (0, 0) and has a rate of change of 5. m: _______ b: ( , ) equation: __________
Write the equation of the line graphed below.
m: _______ b: ( , ) equation: __________
Write the equation of the line represented in the table below.
x y
-3 2
0 4
3 6
6 8
m: _______ b: ( , ) equation: __________
Write the equation of the line graphed below.
m: _______ b: ( , ) equation: __________
Write the equation of the line represented in the table below.
x y
-8 32
-4 24
0 16
4 8
m: _______ b: ( , ) equation: __________
Unit 4 – Writing Linear Equations 7
Examples:
Horizontal Line
y = 5
m: ____________
Vertical Line
x = 5
m: ____________
Write the equation of a vertical line through the point (2, -4). equation: __________
Write the equation of line with slope 0 and passing through the point (3,5). equation: __________
Write the equation of line with undefined slope and passing through the point (-4,8). equation: __________
Write the equation of a horizontal line through the point (-1, 5). equation: __________
Unit 4 – Writing Linear Equations 8
Unit 4 – Writing Linear Equations 9
Slope-Intercept Form: Given Slope and a Point on the Line
Slope – Intercept Form: y = mx + b
m: slope
b: y-intercept
Point – Slope Form: y – y1 = m (x – x1)
m: slope
(x1, y1): any point
Examples:
Write the equation of line with slope 4 and passing through the point (-3, 8 ). m: _______ b: ( , ) equation: __________
Write the equation of line with slope -3/2 and passing through the point (-4, -8). m: _______ b: ( , ) equation: __________
Practice:
Write the equation of line with slope -2 and passing through the point (5,7). m: _______ b: ( , ) equation: __________
Write the equation of line with slope 2/5 and passing through the point (10, -1). m: _______ b: ( , ) equation: __________
Unit 4 – Writing Linear Equations 10
Examples: Write the equation of line passes through (-6,4) and (4, -1). m: _______ b: ( , ) equation: __________
Write the equation of the line represented in the table below.
x y
-2 1
2 -5
6 -11
10 -17
m: _______ b: ( , ) equation: __________
Practice: Write the equation of line passes through (-5,-6) and (0,-3). m: _______ b: ( , ) equation: __________
Write the equation of the line represented in the table below.
x y
5 -3
10 -4
15 -5
20 -6
m: _______ b: ( , ) equation: __________
Continued…
Unit 4 – Writing Linear Equations 11
Write the equation of line with undefined slope and passing through the point (4,-3). equation: __________
Write the equation of line with slope 0 and passing through the point (-2, 9). equation: __________
Write the equation of a vertical line through the point (-5, 0). equation: __________
Write the equation of a horizontal line through the point (-5, -2). equation: __________
Find the equation of a line that crosses the y-axis at the point (0, 3) and has a rate of change of -4. equation: __________
Write the equation of line passes through (8,3) and (-4,-6). equation: __________
Write the equation of the line represented in the table below.
x y
-6 7
-4 4
-2 1
0 -2
equation: __________
Write the equation of the line represented in the table below.
x y
3 12
4 9
5 6
6 3
equation: __________
Unit 4 – Writing Linear Equations 12
Unit 4 – Writing Linear Equations 13
Point-Slope Form: Given Slope and a Point on the Line
Slope – Intercept Form:
y = mx + b
m: slope
b: y-intercept
Point – Slope Form:
y – y1 = m (x – x1)
m: slope
(x1, y1): any point
Examples:
Write the equation of line with slope 2/5 and passing
through the point (7,-3).
m: _______ point: ( , )
equation: _______________
Write the equation of the line graphed below:
m: _______ point: ( , )
equation: _______________
Practice:
Write the equation of line with slope -2/7 and
passing through the point (-5, 8).
m: _______ point: ( , )
equation: _______________
Write the equation of the line graphed below:
m: _______ point: ( , )
equation: _______________
Unit 4 – Writing Linear Equations 14
Examples:
Write the equation of line passes through
(3,-8) and (-2,7).
m: _______ point: ( , )
equation: _______________
Write the equation of the line represented in the
table below.
x y
-5 5
-3 9
-1 13
1 17
m: _______ point: ( , )
equation: _______________
Graph the equation y + 8 = -2(x – 9).
A private music teacher charges $20 per hour, plus
an additional cost for renting the room. If the
teacher charged $95 total for 4 hours, which
equation in point-slope form best represents this?
A. y – 4 =20(x – 95)
B. y – 95 =20(x – 4)
C. y – 4 =95(x – 20)
D. y – 20 =95(x – 4)
Unit 4 – Writing Linear Equations 15
Practice:
Write the equation of line passes through
(-1,-2) and (5,1).
m: _______ point: ( , )
equation: _______________
Write the equation of line passes through
(4,5) and (-5,11).
m: _______ point: ( , )
equation: _______________
Graph the equation y – 1 = 3/4(x – 8).
A pizza company charges $12 per pizza, plus an
additional cost for delivery. If the company
charged $52 total for 4 pizzas, which equation in
point-slope form best represents this?
A. y + 4 =12(x + 52)
B. y + 52 =12(x + 4)
C. y – 4 =12(x – 52)
D. y – 52 =12(x – 4)
Write the equation of the line represented in the
table below.
x y
-8 -22
-3 -12
2 -2
7 8
m: _______ point: ( , )
equation: _______________
Unit 4 – Writing Linear Equations 16
Slope-Intercept Form to Standard Form
Slope – Intercept Form: y = mx + b
Standard Form: Ax + By = C
Examples:
y= 2x – 8 Standard form: __________ x-int ( , ) y-int ( , )
y= 1/3x + 3 Standard form: __________ x-int ( , ) y-int ( , )
y= -3/5x – 18 Standard form: __________ x-int ( , ) y-int ( , )
Unit 4 – Writing Linear Equations 17
Practice:
y= 1/2x – 3 Standard form: __________ x-int ( , ) y-int ( , )
y= -5/2x + 10 Standard form: __________ x-int ( , ) y-int ( , )
y= -4x – 16 Standard form: __________ x-int ( , ) y-int ( , )
y= 3/5x – 12 Standard form: __________ x-int ( , ) y-int ( , )
y= -2/3x – 18
Standard form: __________ x-int ( , ) y-int ( , )
y= 1/8x – 4 Standard form: __________ x-int ( , ) y-int ( , )
Unit 4 – Writing Linear Equations 18
Unit 4 – Writing Linear Equations 19
Extra Practice
Slope – Intercept Form:
y = mx + b
Standard Form:
Ax + By = C
Point – Slope Form:
y – y1 = m (x – x1)
Examples:
Write the equation of line passes through
(-1,-2) and (5,1) in POINT-SLOPE form.
equation: _______________
Write the equation of the line represented in the
table below in SLOPE-INTERCEPT form.
x y
3 12
4 9
5 6
6 3
equation: __________
Write the equation of a vertical line through the
point (-5, 0).
equation: __________
Write the equation of line with slope 0 and passing
through the point (-2, 9).
equation: __________
Write the equation of line with x-intercept
(5,0) and y-intercept (0,-4) in STANDARD form.
Unit 4 – Writing Linear Equations 20
START
FINISH
Unit 4 – Writing Linear Equations 21
Slope-Intercept Form: Parallel and Perpendicular Lines
Slope – Intercept Form:
y = mx + b
Standard Form:
Ax + By = C
Point – Slope Form:
y – y1 = m (x – x1)
Parallel Slopes are ____ ________ !
Perpendicular Slopes are ____________ _____________ !
Examples:
A. y = -3/2x – 3
B. y = -2/3x – 3
C. y = 3/2x + 4
D. y = 2/3x + 4
Which of the equations is parallel to the line above?
Which of the equations is perpendicular to the line above?
Write the equation of the line parallel to the one in
the table with a y-intercept (0,-7) in SLOPE-
INTERCEPT form.
x y
2 -5
6 -7
10 -9
14 -11
Equation: ______________
Write the equation of a line perpendicular to
y = -7/3x + 9 with a y-intercept of (0,-5/7) in
STANDARD form.
A line passes through the points (2,5) and (4,8).
Write the equation of a line parallel to it with a y-
intercept of -5 in SLOPE-INTERCEPT form.
Unit 4 – Writing Linear Equations 22
Practice:
A. y = 1/2x – 2
B. y = -1/2x – 2
C. y = -2x + 1
D. y = 2x + 1
Which of the equations is parallel to the line above?
Which of the equations is perpendicular to the line above?
Write the equation of the line perpendicular to the one in the
table with a y-intercept (0,4) in SLOPE-INTERCEPT form.
x y
2 -5
6 -8
10 -11
14 -14
Equation: ______________
Write the equation of a line parallel to y=-5/6x-3 and y-
intercept (0, 1/6) in STANDARD form.
A line passes through the points (2,-5) and (5,7). Write the
equation of a line perpendicular to it with a y-intercept of 3 in
SLOPE-INTERCEPT form.
Write the equation of the line parallel to
y = -6x+1 through the point (2,-5).
Decide True or False about y = -3x – 5
_____ -3 is the slope
_____ -3 is the x-intercept
_____ -3 is the y-intercept
_____ -5 is the y-intercept
_____ This graph has a shift UP from y=x
_____ There is a positive rate of change
_____ (0,-5) is a point on this line
_____ This graph has a negative slope