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Chapter Five - Algebra

Chapter Five - Algebra. Big Ideas. Lesson 1 Linear Functions. Linear functions describe numerous real-world situations that involve constant rates of change (slope), such as cost, distance, and speed. In a linear function, a constant change in x corresponds to a constant change in y.

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Chapter Five - Algebra

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  1. Chapter Five - Algebra Big Ideas

  2. Lesson 1 Linear Functions • Linear functions describe numerous real-world situations that involve constant rates of change (slope), such as cost, distance, and speed. • In a linear function, a constant change in x corresponds to a constant change in y. • The STANDARD FORM of a linear equation is Ax + By = C. • The graph of a linear function is a line.

  3. Lessons 2,3,4 - Slope and Intercepts • SLOPE is the constant rate of change shown by a line. • SLOPE = change in y / change in x = y2 – y1 / x2 – x1 The x-intercept is the x-coordinate of the point where the graph crosses the x-axis (where y = 0). The y-intercept is the y-coordinate of the point where the graph crosses the y-axis (where x = 0).

  4. Lesson 5 Direct Variation • Many real-world relationships involve direct variations, including relationships in science, cooking, and medicine. • When the dependent variable y depends only on the value of the independent variable x, the linear relationship is a direct variation, written in the form y = kx, where k is the constant of variation. (Direct variation contains only multiplication and always has a y-intercept of 0).

  5. Lessons 6 and 7 – Forms of Linear Equations • Linear equations can be written in Slope-Intercept Form, Point-Slope Form, or Standard Form.

  6. Lesson 8 Slopes of Parallel and Perpendicular Lines • Parallel lines have the same slope. • The slopes of perpendicular lines have a product of -1.

  7. Lesson 9 Transforming Linear Functions • For the function f(x) = mx + b (also known as y = mx + b): • A change in b (the y-intercept) results in a translation (slide). • A change in m (the slope) results in a rotation (turn). • Multiplying m (the slope) by -1 results in a reflection (flip) across the y axis.

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