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Linear Functions
Vocabulary for Algebra I - Linear Functions
| Question | Answer |
|---|---|
| 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
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