Vocabulary for Algebra I - Linear Functions
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Linear Equation | An equation whose graph forms a straight line
p.256
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| Linear Function | A function represented by a linear equation
p.256
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| For any linear equation in two variables (like y=mx+b), all points on it's graph are... | solutions to the equation, and all solutions to the equation appear on the graph.
p.257
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| Standard Form | Ax + By = C
Where A, B and C are real numbers and A and B are not both zero.
It is useful to find x- and y-intercepts.
p.258
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| In a linear equation in two variables (like x and y) - for the equation to be linear, the three things to look for are: | 1) x and y both have exponents of 1
2) x and y are not multiplied together
3) x and y do not appear in denominators, exponents, or radical signs
p.259
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| y-intercept | The y-coordinate of any point where a graph intersects the y-axis. The x-coordinate of this point is always zero.
p.263
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| x-intercept | The x-coordinate of any point where a graph intersects the x-axis. The y-coordinate of this point is always zero.
p.263
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| rate of change | Ratio that compares the amount of change in a dependent to an independent variable.
change in dependent variable (y)
m = ----------------------------------------------
change in independent variable (x)
p.272
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| rise | the difference in the y-values of two points on a line
p.272
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| run | the difference in the x-values of two points on a line
p.272
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| slope of a line (m) | the ratio of rise to run for any two points on a line
rise
m = ----------
run
p.272
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| Slope Formula | Y2 - Y1
m = ---------------
X2 - X1
where (X1, Y1) and (X2, Y2) are two points on the line
p.272
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| Positive Slope | Line rises from left to right
p.273
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| Negative Slope | Line falls from left to right
p. 273
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| Zero Slope | Horizontal line (like the floor)
p.273
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| Undefined Slope | Vertical line (like a wall)
p.273
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| Steepness of a slope | The bigger the absolute value of the slope, the steeper the slope. Slope of 4 is steeper up-slope than a slope of 1/2
Slope of -2 is steeper down-slope than a slope of -1
Slope of -3 is steeper than a slope of 3/4
p.275
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| Direct Variation | A special kind of linear relationship that can be written in the form:
y = kx
They always pass through the origin when graphed.
p.282
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| Constant of Variation | In a direct variation, it is the non-zero constant value for "k" in the form:
y = kx
It is also the slope for the graph of the function and describes the rate of change.
p.282
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| y k = ------ x | Formula to determine the constant of variation, and also the method for determining if a table of data is a Direct Variation (if the ratio is the same for every data pair)
p.283
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| Slope - Intercept Form of a Linear Equation | y = mx + b
where "m" is the slope of the equation's graph and "b" is the y-intercept
p. 291
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| Point - Slope Form of a Linear Equation | y - y1 = m(x-x1)
where "m" is the slope of the equation's graph and (x1, y1) are a point contained on the line
p.298
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| Parallel Lines | Lines in the same plane that have no points in common - they never intersect
p.304
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| Slopes of Parallel Lines | Slopes of parallel lines are equal - non-vertical lines must be parallel if they have the same slope
p. 304
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| Perpendicular Lines | Lines that intersect to form right angles (90-degrees)
p.306
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| Slopes of Perpendicular Lines | Slopes of perpendicular lines are opposite inverse of each other - non-vertical lines must be perpendicular if the product of their slopes is -1
p.306
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