4x 3y = 12 · alg ib chapt 69 exam review.notebook 4 june 04, 2012 linear equations summary...

Alg IB Chapt 69 Exam Review.notebook

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June 04, 2012

Finding slope

riserun

y2 y1x2 x1slope = =

Red:

pick 2 points that are on grid, then use the slope formula

Find the slope of a line that goes through C(2, 5) and D(4, 7).

Green:

Special SlopesHorizontal lines Vertical lines

SlopeIntercept Form of a Linear Equation:

y = mx + b

slope of line yintercept(where graph crosses yaxis)

Identifying slope and yintercept:

1)y = 5x 4 2) y = 2/3x m=b=

m=b=

4) m = 5/2, b = 3

Writing an equation when given m and b:


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June 04, 2012

Graphing from Slopeintercept Form

1) y = 3x + 2Steps:• identify m and b• put a point at b (on y-axis• from that point, use to find more points• connect points

Standard Form of a Linear Equation:

Ax + By = Cwhere A, B, and C are real #'s and A and B are not both zero

Finding x and yintercepts:

x-int• plug 0 in for y• solve for x

y-int• plug 0 in for x• solve for y

Find the x and yintercepts, then graph the equation

4x 3y = 12


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June 04, 2012

• clear fractions• get x and y on same side (Ax + By = C)

Write and equation in Standard Form (given slopeintercept)

y = x 623

y y1 = m(x x1)

(x1, y1) can be any point on the line

slope of line

y 6 = (x + 3)23

PointSlope Form

Write the equation of the line that passes through the points (1, 2), (5, 6)


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June 04, 2012

Linear Equations Summary

SlopeIntercept Form Standard Form Pointslope Form

y = mx + b Ax + By = C y y1 = m(x x1)

m is slope A and B not both 0 (x1, y1) is a pt. on graphb is y intercept m is slope

y = 2/3 x + 5/3 2x + 3y = 5 y 1 = 2/3(x 1)

use "coverup" method to find x & yintercepts

Slopes of Perpendicular Lines

• the slopes of perpendicular lines are opposite reciprocals of one another

• the product of the slopes of perpendicular lines is 1

• ex: y = 4/3x 5 y = 3/4x + 6

Write an equation for the line that is perpendicular to the given line that passes through the given point.

y = 3/4x + 1; (1, 8)

Steps:• identify slope of new line• write equation in point-slope form• convert to slope-intercept form


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June 04, 2012

Slopes of Parallel Lines

• nonvertical lines are parallel if the have the same slope and different yintercepts

• any two vertical lines are parallel

ex: y = 2/3x 5 and y = 2/3x +3

Write an equation for a parallel line, given original equation and a point on the line

Steps• find m in given equation• plug "m" and the point into point-slope form (for the new equation)• convert to slope-intercept form

y = 3/2x + 5 ; (3, 6)

To solve a system of linear equations:~graph both equations on the same coordinate plane~their intersection (a point) is your solution

slope-intercept form!graph using y-int and slope

Solution:

y = x 1

y = 2x 3


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June 04, 2012

Standard FormGraph using intercepts! (cover-up)

x + 2y = 4

3x + y = 3

x + 2y = 4

3x + y = 3

Solution:

Solution:

Solving Systems of Equations by Substitution

1) y = x+1 y = 2x 1

method #2Steps:1) put both equations in slope-int form2) set both equations equal to one another (no more y's!)3) solve for x4) plug your x value into ONE of the equations and solve for y5) write solution AS A COORDINATE (x, y)6) mentally check your solution


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June 04, 2012

7.3 Day 1 Solving Systems by Eliminationmethod #3

(probably your favorite)

Steps:1) equations should be in standard form- Ax + By = C2) make sure equations are "lined up"3) add the columns (one variable should cancel)4) solve for other variable5) substitute into ONE of equations to get other variable's value6) write answer as (x,y) and mentally check :)

2x + 3y = 11 2x + 9y = 1

Spring Lake High School as sold 500 tickets to the musical. A student ticket costs $3 and an adult ticket costs $5. Total ticket sales equals $2100. How many students and adults will be attending?

Breaking Eventhe point at which a business' income (I) equals its expenses (E)after the break even point they will make moneycreate one equation for income and one for expenses, their intersection is the break even point

As a summer job, Hunter starts a typing service. He buys a new computer for $1750. He decides to charge $5.50 per page for typing. Expenses for ink, paper, and electricity are estimated to be $0.50 per page. How many pages must Hunter type to break even?


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June 04, 2012

Linear inequalities: line graphs with shading above or below the line

STEPS

1) make sure y by itself to graph2) graph the line(solid or dotted)3) know symbol

* y < or ≤ means y is smaller, shade below the line

* y > or ≥ means y is bigger, shade above the line

Graph y > 2/3x 3

< or > dotted line< or > solid line

y > x 2

y < 3x + 4

Graphing a system of linear inequalities


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June 04, 2012

4x 3y = 12 · alg ib chapt 69 exam review.notebook 4 june 04, 2012 linear equations summary...

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