Important Rules:Standard Form

Ax + By = C

Rules:• A is positive• A,B,C are whole #s• No fractions/decimals

Example 1Convert the equation to standard form:

y = 2x + 4

-2x -2x

-2x + y = 4

-1 -1 -1

2x – y = -4

*To make A positive, divide *To make A positive, divide (or multiply) (or multiply) everythingeverything by -1 by -1

Example 2Write an equation in standard form:

m = 3/2 b = 12

y = 3x + 12

2

-3/2x -3/2x

-3x + y = 12

2

-3x + 2y = 24

-1 -1 -1

3x – 2y = -24

(2)(2)(2)(2)(2)(2)

Plug into y = mx + bPlug into y = mx + b

*To get rid of the fraction, *To get rid of the fraction, multiply everything by the multiply everything by the denominator.denominator.

Writing Writing Equations of a Equations of a

LineLine

Various Forms of an Equation of a Line.

Slope-Intercept Slope-Intercept FormForm

Standard Standard FormForm

Point-Slope Point-Slope FormForm

slope of the line

intercept

y mx b

m

b y

, , and are integers

0, must be postive

Ax By C

A B C

A A

1 1

1 1

slope of the line

, is any point

y y m x x

m

x y

SOLUTIONSOLUTION

Write an equation given the slope and Write an equation given the slope and yy-intercept-interceptEXAMPLE 1EXAMPLE 1

From the graph, you can see that the slope is From the graph, you can see that the slope is m m = = and the and the yy--intercept is intercept is b =b = –2. –2. Use slope-intercept form Use slope-intercept form to write an equation of the line.to write an equation of the line.

3344

y y == mmx x ++ bb Use slope-intercept form.Use slope-intercept form.

y y == x +x + (–2(–2))3344

Substitute for Substitute for mm and and –2–2 for for bb..33

44

y y == x x ((–2–2))3344

Simplify.Simplify.

Write an equation given two pointsWrite an equation given two points

EXAMPLE 2EXAMPLE 2

Write an equation of the line that passes Write an equation of the line that passes through through (5, –2) (5, –2) and and (2, 10).(2, 10).

SOLUTIONSOLUTION

The line passes through The line passes through ((xx11, , yy11) = (5,–2)) = (5,–2) and and

((xx22, , yy22) = (2, 10).) = (2, 10). Find its slope. Find its slope.

yy22 – – yy11mm ==xx22 – – xx11

10 – (–2)10 – (–2) ==

22 – – 55 1212 – –33== = –4= –4

Write an equation given two pointsWrite an equation given two points

EXAMPLE 2EXAMPLE 2

You know the slope and a point on the line, so use You know the slope and a point on the line, so use point-slope form with either given point to write an point-slope form with either given point to write an equation of the line. Choose equation of the line. Choose ((xx11, , yy11) = (4, – 7).) = (4, – 7).

yy22 – – yy11 == mm((x x –– xx11)) Use point-slope form.Use point-slope form.

yy –– 1010 == –– 44((x x –– 22)) Substitute for Substitute for mm, , xx11,, and and yy11..

y y –– 10 = – 410 = – 4x x + 8+ 8 Distributive propertyDistributive property

Write in slope-intercept form.Write in slope-intercept form.y = – 4y = – 4x x + 8+ 8

Steps for Solving Two-Step Equations

1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation.

2. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

Opposite Operations

Addition Subtraction

Multiplication Division

Helpful Hints?

Identify what operations are on the variable side. (Add, Sub, Mult, Div)

“Undo” the operation by using opposite operations.

Whatever you do to one side, you must do to the other side to keep equation balanced.

Ex. 1: Solve 4x – 5 = 11

4x – 5 = 15 +5 +5 (Add 5 to both sides)4x = 20 (Simplify) 4 4 (Divide both sides

by 4)x = 5 (Simplify)