standard form solve equations
DESCRIPTION
solving equationsTRANSCRIPT
![Page 1: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/1.jpg)
Important Rules:Standard Form
Ax + By = C
Rules:• A is positive• A,B,C are whole #s• No fractions/decimals
![Page 2: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/2.jpg)
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
![Page 3: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/3.jpg)
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.
![Page 4: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/4.jpg)
Writing Writing Equations of a Equations of a
LineLine
![Page 5: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/5.jpg)
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
![Page 6: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/6.jpg)
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.
![Page 7: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/7.jpg)
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
![Page 8: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/8.jpg)
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
![Page 9: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/9.jpg)
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.
![Page 10: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/10.jpg)
Opposite Operations
Addition Subtraction
Multiplication Division
![Page 11: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/11.jpg)
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.
![Page 12: Standard form solve equations](https://reader035.vdocuments.pub/reader035/viewer/2022081515/55896d34d8b42ab34f8b474e/html5/thumbnails/12.jpg)
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)