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# Solving linear equations alg 2 project anna jen ali

## on Mar 27, 2011

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## Solving linear equations alg 2 project anna jen aliPresentation Transcript

• Solving Linear Equations
By: Anna Carey, Ali LaBella, and Jen Putnam
• Linear Equations vs.Linear Functions
A linear equationis an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.
• Examples of Linear Equations
Linear EquationsNot Linear Equations
7x − 3y = 14 8a + 3b2 = -12
x = 11y=ghghjgfj
3s = -2t − 9x + xy= 2
y = ¼xy = 1/X
• Linear Equations cannot…
• Be raised to a power other than 1
• Cannot have two variables multiplied by each other
Why?
• Ax + By = C
• A must be greater than or equal to zero
• A and B cannot be zero
• Example: 5x + 7y = 12
Standard Form
• y = mx + b
• m is the slope of the line
• b is the y-intercept
• Example: y = ¾x + 6
Slope-Intercept Form
• y − y1 = m(x − x1)
• (x1 , y1) are the coordinates of a point on the line
• m is the slope of the line
• Example: y +1 =¼(x − 2)
Point-Slope Form
• x/a+y/b = 1
• a is the x-intercept
• b is the y-intercept
• Example: x/2 + y/5 = 1
Intercept Form
• Slope is the ratio of the change in
y-coordinates to the change in x-coordinates.
(Rise over Run, Rate of Change)
y2− y1= m
x2− x1tghr
What is slope?
• The x-intercept is where the line crosses the
x-axis.
• Set y equal to zero
• Example: 4x + 2y = 8
4x + 2(0) = 8
4x = 8
x = 2
• So, the x-intercept is (2, 0)
Finding the x-intercept
• The y-intercept is where the line crosses the
y-axis.
• Set x equal to zero
• Example: 4x + 2y = 8
4(0) + 2y= 8
2y = 8
y = 4
• So, the y-intercept is (0, 4)
Finding the y-intercept
• Solve: 3x − 4 = -10
Isolate the variable, x
• 3x − 4 (+ 4) = -10 (+ 4)
• 3x = -6
• x = -2
The solution to this linear equation is x = -2
Solving a Linear Equation
• THE END