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Linear Functions

Vocabulary for Algebra I - Linear Functions

Linear Equation An equation whose graph forms a straight line p.256
Linear Function A function represented by a linear equation p.256
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
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
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
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
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
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
rise the difference in the y-values of two points on a line p.272
run the difference in the x-values of two points on a line p.272
slope of a line (m) the ratio of rise to run for any two points on a line rise m = ---------- run p.272
Slope Formula Y2 - Y1 m = --------------- X2 - X1 where (X1, Y1) and (X2, Y2) are two points on the line p.272
Positive Slope Line rises from left to right p.273
Negative Slope Line falls from left to right p. 273
Zero Slope Horizontal line (like the floor) p.273
Undefined Slope Vertical line (like a wall) p.273
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
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
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
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
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
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
Parallel Lines Lines in the same plane that have no points in common - they never intersect p.304
Slopes of Parallel Lines Slopes of parallel lines are equal - non-vertical lines must be parallel if they have the same slope p. 304
Perpendicular Lines Lines that intersect to form right angles (90-degrees) p.306
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
Created by: gklee