266 Chapter 3 Graphing Linear Equations in Two Variables Vocabulary and Key Concepts Ax By C 1. a. The standard form of an equation of a line is , where A and B are not both zero and C is y-intercept Review Exercises For Exercises 2–6, graph each equation. y y1 m(x x1) 2. 5x 15 0 3. 2x 3y 3 4. y 2x 5. 6. y 11. 25x 2 15 5 0 5 4 y 1 5 4 y 1 23 543 1 2 3 4 5 2524 1 2 3 4 5 2221 22 23 24 25 21 y 1 21 11, 32 and 12, 62 9 12, 42 and 12, 42 2 horizontal vertical 12, 52 and 15, 52 0 16.1, 2.52 and 16.1, 1.52 Undefined The slope is 3, and the line passes through the point 12, 12. 13. The slope is , and the line passes through the point 4 12 15. The 1slope 02. is , and the line passes through 1, 13, 22. x 3 2 21 2 3 4 5 x 3 2 1 2x 3y 3 5 4 y 1 543 1 2 3 4 5 5 4 y 1 21 543 1 2 3 4 5 2 1 2 3 4 5 x 3 2 1 y x 4 5 2 3 4 5 x 3 2 1 y 2x 543 1 2 3 4 5 2 3 4 5 6 7 8 x 2 1 3 y 9 4 5 3 y 9 x For Exercises 7–10, find the slope of the line that passes through the given points. 7. 8. 9. 10. slope Concept 1: Writing an Equation of a Line Using the Point-Slope Formula For Exercises 11–16, use the point-slope formula (if possible) to write an equation of the line given the following information. (See Example 1.) 2 11, 52. y 3x 7 or 3x y 7 y 2x 3 or 2x y 3 y 4x 14 or 4x y 14 12. The slope is , and the line passes through the point 5, 14. The slope is and the line passes through the point 34 16. The 12,02. slope is , and the line passes through 11, 32. y 5x 2 or 5x y 2 1 2 y x or x 2y 1 1 2 3 4 y x or 3x 4y 6 3 2 Writing Translating Expression Geometry Scientific Calculator Video a constant. b. A line defined by an equation y k, where k is a constant is a (horizontal/vertical) line. c. A line defined by an equation x k, where k is a constant is a (horizontal/vertical) line. d. Given the slope-intercept form of an equation of a line, y = mx b, the value of m is the and b is the . e. Given a point (x1, y1) on a line with slope m, the point-slope formula is given by .
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