Unit 4 - algebra1kraus / Home Page 4 Notebook.pdfUnit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 ... -4 4 -2 1 0 -2 equation: _____ Write the equation of the

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


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

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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?


Critical Vocabulary

Slope

x-Intercept / Zero

y-intercept

Slope-Intercept Form

Point-Slope Form

Standard Form


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: __________


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: __________


m: _______ b: ( , ) equation: __________


x y

-3 2

0 4

3 6

6 8

m: _______ b: ( , ) equation: __________


m: _______ b: ( , ) equation: __________


x y

-8 32

-4 24

0 16

4 8

m: _______ b: ( , ) equation: __________


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: __________



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: __________


Examples: Write the equation of line passes through (-6,4) and (4, -1). m: _______ b: ( , ) equation: __________


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: __________


x y

5 -3

10 -4

15 -5

20 -6

m: _______ b: ( , ) equation: __________

Continued…


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: __________


x y

-6 7

-4 4

-2 1

0 -2

equation: __________


x y

3 12

4 9

5 6

6 3




Point-Slope Form: Given Slope and a Point on the Line


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: _______________


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)


Practice:


(-1,-2) and (5,1).

m: _______ point: ( , )

equation: _______________


(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)


table below.

x y

-8 -22

-3 -12

2 -2

7 8

m: _______ point: ( , )

equation: _______________


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 ( , )


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= -2/3x – 18

Standard form: __________ x-int ( , ) y-int ( , )




Extra Practice


y = mx + b

Standard Form:

Ax + By = C


y – y1 = m (x – x1)

Examples:


(-1,-2) and (5,1) in POINT-SLOPE form.

equation: _______________


table below in SLOPE-INTERCEPT form.

x y

3 12

4 9

5 6

6 3


Write the equation of a vertical line through the

point (-5, 0).


Write the equation of line with slope 0 and passing

through the point (-2, 9).


Write the equation of line with x-intercept

(5,0) and y-intercept (0,-4) in STANDARD form.


START

FINISH


Slope-Intercept Form: Parallel and Perpendicular Lines


y = mx + b

Standard Form:

Ax + By = C


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.


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

Documents

Unit 4 - algebra1kraus / Home Page 4 Notebook.pdfUnit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 ... -4 4 -2 1 0 -2 equation: _____ Write the equation of the