Finding Linear Equations - Battaly · College Algebra Home Page1.5 Finding Linear Equations Class...

Finding Linear Equations

© G. Battaly, 2013 1

February 06, 2013

1.5 Finding Linear Equations

College Algebra Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Study 1.5 # 1 15, 21,25,29, 33, 41, 45, 4955, 59, 63, 67

Homework Problems

http://www.battaly.com/collegealgebra

http://www.battaly.com/collegealgebra/homework/1_5_linearequations.htm



February 06, 2013



2. Substitute m = 2: ______________

Given: m = 2, (0, 1) Find: equation of line

1. Start withSlopeintercept Form: ______________

3. (0,1) is yintercept Substitute b = 1: ______________

geogebra, interactive: slopeintercept form, y = mx + bhttp://www.battaly.com/collegealgebra/geogebra/slopeIntercept/


Homework Problems


http://www.battaly.com/collegealgebra/geogebra/slopeintercept/




February 06, 2013



2. Substitute m = 2: y = 2x + b


1. Start withSlopeintercept Form: y = mx + b

3. (0,1) is yintercept Substitute b = 1: y = 2x 1

Previous example:



2. Substitute m = (1/3): _________________

Given: m = (1/3), (0, 0.1) Find: equation of line

1. Start withSlopeintercept Form: _________________

3. (0,0.1) is yintercept Substitute b = 0.1: _________________

Homework Problems






February 06, 2013


Class Notes: Prof. G. Battaly, Westchester Community College, NYgeogebra, interactive: slopeintercept form, y = mx + bhttp://www.battaly.com/collegealgebra/geogebra/slopeIntercept/


2. Substitute m = (1/3): y = (1/3)x + b

Given: m = (1/3), (0, 0.1) Find: equation of line1. Start withSlopeintercept Form: y = mx + b

3. (0,0.1) is yintercept Substitute b = 0.1: y = (1/3)x + 0.1



1. Start withSlopeintercept Form: y = mx + b

3. (0,1) is yintercept Substitute b = 1: y = 2x 1

Previous example:

Homework Problems






February 06, 2013




2. Substitute m = 2: ______________


1. Start withSlopeintercept Form: ______________

3. (1, 0) is NOT a yintercept ? Substitute b =? ______________

Homework Problems






February 06, 2013





Given: m = 2, (1, 0) Find: equation of line1. Start withSlopeintercept Form: y = mx + b

3. (1, 0) is NOT a yintercept ? Substitute b =? y = 2x + ?

How can we find b? y = 2x + bWe need to solve the equation for b.

y = 2x + bWhat can we use?

Do we have a solution (x1, y1) that we can substitute?

Yes!! Substitute the solution (1, 0)

Homework Problems






February 06, 2013




How can we find b? y = 2x + b

We need to solve the equation for b.y = 2x + b

What can we use?Do we have a solution (x1, y1)

that we can substitute?

Yes!! Substitute the solution (1, 0) Substitute the solution (1,0) or let x=1 and y=0: 0 = 2(1) + bthen: 0 = 2 + band: b = 2

Finally, Substitute b= 2 y = 2x 2

y = 2x + b


Homework Problems






February 06, 2013




Do even problems:

Given: m = __, (___, ___) Find: equation of line

Homework Problems





© G. Battaly, 2013 10

February 06, 2013




Do even problems:


Homework Problems





© G. Battaly, 2013 11

February 06, 2013




(x,y) represents any point on the line, each of which is a solution to the equation


Start: m = y2 y1 x2 x1 Replace (x2,y2) with (x,y): m = y y1 x x1

A different approach for problems:Given: m = __, (___, ___) Find: equation of line

Multiply both members of eq. by (x x1): (x x1) m = y y1 (x x1) x x1 Simplify: (x x1) m = (y y1)

Rewrite: (y y1) = m(x x1)

Homework Problems





© G. Battaly, 2013 12

February 06, 2013




(x,y) represents any point on the line, each of which is a solution to the equation


Start: m = y2 y1 x2 x1 Replace (x2,y2) with (x,y): m = y y1 x x1

A different approach for problems:Given: m = __, (___, ___) Find: equation of line

Multiply both members of eq. by (x x1): (x x1) m = y y1 (x x1) x x1 Simplify: (x x1) m = (y y1)

Rewrite: (y y1) = m(x x1)

Point Slope Form of Linear Equation: (y y1) = m (x x1) Nonvertical line, (x1,y1) point on the line

Homework Problems





© G. Battaly, 2013 13

February 06, 2013




Do even problems:


Homework Problems





© G. Battaly, 2013 15

February 06, 2013





Start by finding the slope: m = y2 y1 x2 x1

How do find equation when 2 points are given and no slope?

Given: (___, ___) , (___, ___) Find: equation of line

Then use either the SlopeIntercept orthe PointSlope Form of a Linear Equation

Homework Problems





© G. Battaly, 2013 16

February 06, 2013





Start by finding the slope: m = y2 y1 x2 x1

How do find equation when 2 points are given and no slope?

Given: (___, ___) , (___, ___) Find: equation of line

Then use either the SlopeIntercept orthe PointSlope Form of a Linear Equation

Homework Problems





© G. Battaly, 2013 17

February 06, 2013




Do even problems:

Given: (___, ___), (___, ___) Find: equation of line

Homework Problems





© G. Battaly, 2013 18

February 06, 2013




Do even problems:

Given: (___, ___), (___, ___) Find: equation of line

Homework Problems




Finding Linear Equations - Battaly · College Algebra Home Page1.5 Finding Linear Equations Class...

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