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12-5

Slope. 12-5. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Slope. 12-5. Course 2. Warm Up Graph the linear function. y = 2 x + 4. Slope. 12-5. Course 2. Problem of the Day

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12-5

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  1. Slope 12-5 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. Slope 12-5 Course 2 Warm Up Graph the linear function. y = 2x + 4

  3. Slope 12-5 Course 2 Problem of the Day One vertex of a triangle is at the origin. The other two vertices are at the x- and y-intercepts of y = 2x + 10. What is the area of the triangle? 25 square units

  4. Slope 12-5 Course 2 Learn to determine the slope of a line and to graph a line, given one point, the y-intercept, and the slope.

  5. Slope 12-5 Course 2 Insert Lesson Title Here Vocabulary slope y-intercept slope-intercept form

  6. Slope 12-5 y-intercept Course 2 The slope of a line is a measure of its steepness and is the ratio of rise to run: y Run rise Rise slope = x run The y-coordinate of the point where a line crosses the y-axis is called the y-intercept.

  7. Slope 12-5 y-intercept 3 3 rise run slope = = = 1 Course 2 Additional Example 1A: Identifying Slope and y-intercept of a line A. Give the slope and y-intercept of the line. 3 3 The rise is 3. The run is 3. The y-intercept is –4.

  8. Slope 12-5 y-intercept M(1, –1) N(3, –1) 0 2 rise run slope = = = 0 Course 2 Additional Example 1B: Identifying the Slope and y-intercept of a Line B. Give the slope and y-intercept of the line. 2 The rise is 0. The run is 2. The y-intercept is –1.

  9. Slope 12-5 y-intercept 0 –8 rise run slope = = = 0 Course 2 Insert Lesson Title Here Try This: Example 1A A. Give the slope and y-intercept of the line. The rise is 0. The run is –8. The y-intercept is –3. –8 (–4, –3) (4, –3)

  10. Slope 12-5 y-intercept 8 –2 rise run slope = = = –4 Course 2 Insert Lesson Title Here Try This: Example 1B B. Give the slope and y-intercept of the line. (–2, 4) –2 The rise is 8. The run is –2. 8 The y-intercept is –4. (0, –4)

  11. Slope 12-5 y =mx +b Slope y-intercept Course 2 A linear equation with the variable y isolated on the left-hand side of the equation is in slope-intercept form.

  12. Slope 12-5 Course 2 Additional Example 2: Identifying Slope and y-intercept in a Linear Equation Give the slope and y-intercept of each line, given the equation. A. y = 3x – 1 y = 3x – 1 The slope is 3. The y-intercept is –1. 1 2 B. y = x + 2 1 2 y = x + 2 1 2 . The slope is The y-intercept is 2.

  13. Slope 12-5 Course 2 Insert Lesson Title Here Try This: Example 2 Give the slope and y-intercept of each line, given the equation. A. y = 4x – 4 y = 4x – 4 The slope is 4. The y-intercept is –4. 1 3 B. y = x + 3 1 3 y = x + 3 1 3 . The slope is The y-intercept is 3.

  14. Slope 12-5 Course 2 When you know the slope and any one point on a line, you can graph the line.

  15. Slope 12-5 (–1, 3) Course 2 Additional Example 3: Graphing Linear Equations Using Slope and y-intercept Graph each line, given the equation. A. y = –2x + 1 y = –2x + 1 2 –1 The slope is –2 or The y-intercept is 1. From point (0, 1) move 2 units up (rise) and 1 unit left (run) to find another point on the line. Draw a line to connect the points

  16. Slope 12-5 (0, 3) Course 2 Additional Example 3B: Graphing Linear Equations Using Slope and y-intercept Graph the line, given the equation. B. y = 3 y = 0x + 3 The slope is 0. The y- intercept is 3. Locate the point (0, 3). When the slope is zero the line is horizontal. Draw a horizontal line through point (0, 3).

  17. Slope 12-5 (1, –3) (0, –4) Course 2 Insert Lesson Title Here Try This: Example 3A Graph the line, given the equation. A. y = x – 4 y = 1x – 4 The slope is 1. The y-intercept is –4. From point (0, –4) move 1 unit up (rise) and 1 unit right (run) to find another point on the line. Draw a line to connect the points

  18. Slope 12-5 (–3, –1) (0, –1) Course 2 Insert Lesson Title Here Try This: Example 3B Graph the line, given the equation. B. y = –1 y = 0x – 1 The slope is 0. The y- intercept is –1. Locate the point (0, –1). When the slope is zero the line is horizontal. Draw a horizontal line through point (0, –1).

  19. Slope 12-5 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Tell the slope and y-intercept of each line, given the equation. 1.y = x – 5 2.y = 3.y = –2x + 7 1; –5 3 4 3 4 ; 0 x –2; 7

  20. Slope 12-5 Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 1 2 4. Graph the line, given the equation y = x – 2.

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