solving linear equations alg 2 project anna jen ali
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By: Anna Carey, Ali LaBella, and Jen Putnam
SOLVING LINEAR EQUATIONS
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A linear equation is an equation that has no operations other than
addition, subtraction, and multiplication of a variable by a
constant.
LINEAR EQUATIONS
VS.LINEAR
FUNCTIONS
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Linear Equations Not Linear Equations
7x − 3y = 14 8a + 3b2 = -12
x = 11y=ghghjgfj
3s = -2t − 9 x + xy = 2
y = ¼x y = 1/X
EXAMPLES OF LINEAR EQUATIONS
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Linear Equations cannot…• Be raised to a power other than 1• Cannot have two variables multiplied by
each other
WHY?
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Ax + By = C• A must be greater than or equal to zero• A and B cannot be zero• Example: 5x + 7y = 12
STANDARD FORM
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y = mx + b • m is the slope of the line• b is the y-intercept• Example: y = ¾x + 6
SLOPE-INTERCEPT FORM
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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
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x/a + y/b = 1• a is the x-intercept• b is the y-intercept• Example: x/2 + y/5 = 1
INTERCEPT FORM
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• 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?
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• 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
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• 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
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Solve: 3x − 4 = -101. 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
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