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General Form of equation of a line
Ax+By=C
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Slope (steepness) Formula
- m= y2-y1 x2-x1
- m= rise = vertical change run horizontal change
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How do you read the graph?
Left to right
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Falling
m<0 negative, hence y=b
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Horizontal
zero (m=0) hence y=b
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Vertical
Undefined, hence x=a
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Slope intercept form equation
y=mx+b
slope = m
coordinate y= b
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How do we write the equation for slope intercept form?
Isolate y variable so that it is
y= slope (x) + b from given equation
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What is the y-intercept always equivalent to?
the y coordinate
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Point slope formula
Used if you have only one point and the slope
y-y1=m(x-x1)
(does not work for verticle lines)
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How do you find the equation of a line given 2 points?
Use the points to find the slope, and then plug it into the point-slope formula
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How do you tell if lines are parallel
They must have the same slope
m1=m2
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How do you find the equation of a parallel line?
- 1) write slope intercept form
- 2) identify the slope given (parallel lines have same slope)
- 3) substitute slope into equation of the line
- 4) substitute in variables (coordinates given)
- 5) since b is the only variable left, SOLVE FOR B
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What is unique ( and always true) about perpendicular slopes?
The slopes' of the two lines will always be negative reciprocals of eachother
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Which two types of lines do not share the perpendicular slope property?
- horizontal, m=0
- vertical, slope undefined
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How do you find the equation of a perpendicular line?
- 1) Identify the slope of the given line
- 2) identify its reciprocal to find the slope that is perpendicular to given line
- 3) Write equation of the line we are looking for in slope-intercept form y=m2x+b
- 4) substitute the reciprocal slope back into equarion
- 5) plug in coordinates
- 6) since b is the only variable left, SOLVE FOR B
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