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Using Slopes and Intercepts. 11-3. HOMEWORK & Learning Goal. Lesson Presentation. Pre-Algebra. HOMEWORK answers. Page 548 #1-5. Pre-Algebra HOMEWORK. Page 553 #1-8. Our Learning Goal.

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11-3

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  1. Using Slopes and Intercepts 11-3 HOMEWORK & Learning Goal Lesson Presentation Pre-Algebra

  2. HOMEWORK answers Page 548 #1-5

  3. Pre-Algebra HOMEWORK Page 553 #1-8

  4. Our Learning Goal Students will be able to graph linesusing linear equations, understand the slope of a line and graph inequalities.

  5. Our Learning Goal Assignments • Learn to identify and graph linear equations. • Learn to find the slope of a line and use slope to understand and draw graphs. • Learn to use slopes and intercepts to graph linear equations. • Learn to find the equation of a line given one point and the slope. • Learn to recognize direct variation by graphing tables of data and checking for constant ratios. • Learn to graph inequalities on the coordinate plane. • Learn to recognize relationships in data and find the equation of a line of best fit.

  6. Today’s Learning Goal Assignment Learn to use slopes and intercepts to graph linear equations.

  7. Vocabulary x-intercept y-intercept slope-intercept form

  8. You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

  9. 4x = 12 4 4 Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x-intercept and y-intercept of the line 4x – 3y = 12. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 4x – 3y = 12 4x – 3(0) = 12 4x = 12 x = 3 The x-intercept is 3.

  10. -3y = 12 -3 -3 Additional Example 1 Continued Find the y-intercept (x = 0). 4x – 3y = 12 4(0) – 3y = 12 –3y = 12 y = –4 The y-intercept is –4.

  11. Additional Example 1 Continued The graph of 4x – 3y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

  12. 8x = 24 8 8 Try This: Example 1 Find the x-intercept and y-intercept of the line 8x – 6y = 24. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 8x – 6y = 24 8x – 6(0) = 24 8x = 24 x = 3 The x-intercept is 3.

  13. -6y = 24 -6 -6 Try This: Example 1 Continued Find the y-intercept (x = 0). 8x – 6y = 24 8(0) – 6y = 24 –6y = 24 y = –4 The y-intercept is –4.

  14. Try This: Example 1 Continued The graph of 8x – 6y = 24 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

  15. y = mx + b Slope y-intercept In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.

  16. Helpful Hint For an equation such as y = x – 6, write it as y = x + (–6) to read the y-intercept, –6.

  17. Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y-intercepts Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 2x + y = 3 2x + y = 3 –2x–2x Subtract 2x from both sides. y = 3 – 2x Rewrite to match slope-intercept form. y = –2x + 3 The equation is in slope-intercept form. m = –2 b= 3 The slope of the line 2x + y = 3 is –2, and the y-intercept is 3.

  18. Try This: Example 2A Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 4x + y = 4 –4x–4x Subtract 4x from both sides. y = 4 – 4x Rewrite to match slope-intercept form. y = –4x + 4 The equation is in slope-intercept form. m = –4 b= 4 The slope of the line 4x + y = 4 is –4, and the y-intercept is 4.

  19. 5y = x 5 3 3 5 5 y = x + 0 3 m = 5 3 The slope of the line 5y = 3x is , and the y-intercept is 0. 5 Additional Example 2B: Using Slope-Intercept Form to Find Slopes and y-intercepts B. 5y = 3x 5y = 3x Divide both sides by 5 to solve for y. The equation is in slope-intercept form. b = 0

  20. 7y = x 7 2 2 7 7 y = x + 0 2 m = 7 2 The slope of the line 7y = 2x is , and the y-intercept is 0. 7 Try This: Example 2B B. 7y = 2x 7y = 2x Divide both sides by 7 to solve for y. The equation is in slope-intercept form. b = 0

  21. 3y 3 4 –4x 3 3 4 9 3 = + 3 4 y =- x + 3 m =- 3 The slope of the line 4x+ 3y = 9 is – , and the y-intercept is 3. Additional Example 2C: Using Slope-Intercept Form to Find Slopes and y-intercepts C. 4x + 3y = 9 4x + 3y = 9 –4x–4x Subtract 4x from both sides. 3y = 9 – 4x Rewrite to match slope-intercept form. 3y = –4x + 9 Divide both sides by 3. The equation is in slope-intercept form. b= 3

  22. 4y 4 5 –5x 4 4 5 8 4 = + 4 5 y =- x + 2 m =- 4 The slope of the line 5x + 4y = 8 is – , and the y-intercept is 2. Try This: Example 2C C. 5x + 4y = 8 5x + 4y = 8 –5x–5x Subtract 5x from both sides. 4y = 8 – 5x Rewrite to match slope-intercept form. 5x + 4y = 8 Divide both sides by 4. The equation is in slope-intercept form. b= 2

  23. y = – x + 2 3 4 Lesson Quiz Write each equation in slope-intercept form, and then find the slope and y-intercept. 1. 2y – 6x = –10 2. –5y – 15x = 30 Write the equation of the line that passes through each pair of points in slope-intercept form. 3. (0, 2) and (4, –1) 4. (–2, 2) and (4, –4) y = 3x – 5; m = 3; b = –5 y = –3x – 6; m = –3; b = –6 y = –x

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