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22 Cards in this Set
- Front
- Back
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What is an important characteristic of graphed lines?
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slant or steepness
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What is one way to measure the steepness of a line?
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Compare the vertical change in the line with the horizontal change while moving along the line from one fixed point to another.
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Slope
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the measure of steepness of a line. Is the ratio of the vertical change in y to horizontal change in x along a line.
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Rise
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Is the vertical change between two points on a line, that is the change in the y- values.
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Run
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Is the horizontal change between two points on the line, that is the change in x- values
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Slope formula
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Vertical Change (Rise)
____________________ =m Horizontal Change (Run) |
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The slope of a line is the same for any two points on the line, True or False
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True
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How do you find the slope of a line?
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Through two nonspecific points (x₁,x₂) and (y₁,y₂). Read x1, as "x - sub - one", and x2 as "x - sub - two". This notation is called subscript notation.
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Subscript Notation
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Is a way of indication nonspecific values, such as x₁,x₂
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The symbol for slope?
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m
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Slope Formula
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change in y y2 - y1
m = _________ = ______ change in x = x2 - x1 |
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What does the slope tell?
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The slope of a line tells how fast y changes for each unit of x; that is, the slope gives the change in y for each unit change in x.
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Does it matter which piont is (x1,y1) or (x2,y2)?
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No, however be consistent.
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Positive slope
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rises (slants up) from left to right
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Negative slope
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falls (slants down) from left to right
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What is the slope of a horizontal line?
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zero, since the difference in y-values is always 0.
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What is the slope of a vertical line?
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All points on avertical line have the same x-values, so the slope of any vertical line is undefined
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Define parallel lines?
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Two lines in a plane that never intersect.
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How can you tell if two lines are parallel?
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By determining their slopes. Non-vertical lines always have the same slope.
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Define perpendicular lines?
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Two lines that intersect to form a right (90 degree) angle
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How do you determine if two lines are perpendicular?
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This condition is true in general. If the product of the slopes of two perpendicular lines, neither of which is vertical, is always -1. this means that the slopes of perpendicular lines are negative (or opposite) reciprocals.
If one slope is the nonzero number a, the other slope is -1/a. For example: 3/4 -4/3 1/2 -2/1 -6 1/6 -0.4 10/4 |
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what is the Slope-Intercept form of a linear equation with two variables?
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y = mx = b
where; x & y are variables m & b are numbers m = slope b = y-intercept examples: y = 1/2x - 3 m=1/2 y-intercept = -3 y = x + 4 m=1 y-intercept=4 |
