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Vocabulary

Using Slopes and Intercepts. 11-3. Course 3. Insert Lesson Title Here. Vocabulary. x -intercept y -intercept slope-intercept form. Using Slopes and Intercepts. 11-3. Course 3. You can graph a linear equation easily by finding the x -intercept and the

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Vocabulary

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  1. Using Slopes and Intercepts 11-3 Course 3 Insert Lesson Title Here Vocabulary x-intercept y-intercept slope-intercept form

  2. Using Slopes and Intercepts 11-3 Course 3 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).

  3. You MUST know this! • Write this down! • X-intercept, the y-value in the ordered pair is 0 ex: (4,0) which means the line crosses the x-axis at 4. • Y-intercept, the x value in the ordered pair is 0! ex:(0,5) which means the line crosses the y-axis at 5.

  4. To find the intercepts… • To find the x-intercept, substitute 0 for y and solve the equation for x. The answer is your x-intercept. • To find the y-intercept, substitute 0 for x and solve the equation for y. The answer is your y-intercept.

  5. Using Slopes and Intercepts 11-3 4x = 12 4 4 Course 3 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.

  6. Using Slopes and Intercepts 11-3 -3y = 12 -3 -3 Course 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.

  7. Using Slopes and Intercepts 11-3 Course 3 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).

  8. Using Slopes and Intercepts 11-3 8x = 24 8 8 Course 3 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.

  9. Using Slopes and Intercepts 11-3 -6y = 24 -6 -6 Course 3 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.

  10. Using Slopes and Intercepts 11-3 Course 3 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).

  11. Using Slopes and Intercepts 11-3 y = mx + b Slope y-intercept Course 3 In an equation written in slope-intercept form, y = mx + b, mis the slope and bis the y-intercept. (X,Y) come from an ordered pair which lies on the line

  12. Using Slopes and Intercepts 11-3 Helpful Hint Helpful Hint For an equation such as y = x – 6, read the y-intercept as –6 and the slope as 1. When asked to write the equation in slope-intercept form, simply solve for Y and put the ‘x’ term directly to the right of the = sign! This is logical if you look at the formula: y=mx+b What variable is isolated by itself on 1 side of the equation? YES, Y! Course 3

  13. Using Slopes and Intercepts 11-3 Course 3 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 The equation is in slope-intercept form. y = –2x + 3 m = –2 b= 3

  14. Using Slopes and Intercepts 11-3 3 5 y = x + 0 m = 3 5 Course 3 Additional Example 2B: Using Slope-Intercept Form to Find Slopes and y-intercepts B. 5y = 3x The equation is in slope-intercept form. b = 0

  15. Using Slopes and Intercepts 11-3 4 3 4 y =- x + 3 m =- 3 Course 3 Additional Example 2C: Using Slope-Intercept Form to Find Slopes and y-intercepts C. 4x + 3y = 9 The equation is in slope-intercept form. b= 3

  16. Using Slopes and Intercepts 11-3 Course 3 Try This: Example 2A Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 4x + y = 4 y = –4x + 4 The equation is in slope-intercept form. m = –4 b= 4

  17. Using Slopes and Intercepts 11-3 2 7 y = x + 0 m = 2 7 Course 3 Try This: Example 2B B. 7y = 2x 7y = 2x The equation is in slope-intercept form. b = 0

  18. Using Slopes and Intercepts 11-3 5 4 5 y =- x + 2 m =- 4 Course 3 Try This: Example 2C C. 5x + 4y = 8 5x + 4y = 8 The equation is in slope-intercept form. b= 2

  19. Using Slopes and Intercepts 11-3 Course 3 Additional Example 3: Entertainment Application A video club charges $8 to join, and $1.25 for each DVD that is rented. The linear equation y = 1.25x + 8 represents the amount of money y spent after renting x DVDs. Graph the equation by first identifying the slope and y-intercept. The equation is in slope-intercept form. y = 1.25x + 8 NOTE that the initial value is the same as the y-intercept. Initial value in this case is the upfront charge. (Initial, what you start with) m =1.25 b = 8

  20. Using Slopes and Intercepts 11-3 Course 3 Additional Example 3 Continued The slope of the line is 1.25, and the y-intercept is 8. The line crosses the y-axis at the point (0, 8) and moves up 1.25 units for every 1 unit it moves to the right.

  21. Using Slopes and Intercepts 11-3 Course 3 Try This: Example 3 A salesperson receives a weekly salary of $500 plus a commission of 5% for each sale. Total weekly pay is given by the equation S = 0.05c + 500. Graph the equation using the slope and y-intercept. The equation is in slope-intercept form. y = 0.05x + 500 m =0.05 b = 500 (initial value)

  22. Using Slopes and Intercepts 11-3 y 2000 1500 1000 500 x 15,000 10,000 5000 Course 3 Try This: Example 3 Continued The slope of the line is 0.05, and the y-intercept is 500. The line crosses the y-axis at the point (0, 500) and moves up 0.05 units for every 1 unit it moves to the right. 250/5000=.05

  23. Question time! • Can you find the x-intercept and y-intercepts of a line? • Can you graph the intercepts and draw the graphed line? • Can you solve an equation and write it in slope-intercept form? • Do you know the equation for slope-intercept form? • What do ‘m’, ‘b’, ‘x’ & ‘y’ stand for in the slope intercept form equation? • Parallel lines have what kind of slope? • Perpendicular lines have what kind of slope? • What is the slope formula given 2 ordered pair? If you can answer these questions then you’re ready! If not, raise both arms NOW!

  24. What is the equation of the line? The formula for slope-intercept form has 3 names. The formula y=mx+b is called: 1st name: Slope-Intercept Form 2nd name: Equation of a line 3rd name: Standard Form Anytime you are asked to write an equation in slope-intercept form, the equation of a line or standard form, write the equation in y=mx+b form!

  25. So, let’s put what we know so far together… • Given 2 ordered pair and asked to find the equation of the line: (y=mx+b) • Step 1: use the slope formula and find the slope. • Step 2: use the slope intercept formula and plug in the slope and 1 ordered pair and solve the equation for b which is the y-intercept. • Step 3: plug in the slope and y-intercept, leave x and y in the equation and write your answer. (example: y=3x+4)

  26. Using Slopes and Intercepts 11-3 y2 – y1 = x2 – x1 4 – (–4) 8 –1 – 3 –4 = Course 3 Additional Example 4: Writing Slope-Intercept Form Write the equation of the line that passes through (3, –4) and (–1, 4) in slope-intercept form. Find the slope. = –2 The slope is –2. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b Substitute –1 for x, 4 for y, and –2 for m. 4 = –2(–1) + b 4 = 2 + b Simplify.

  27. Using Slopes and Intercepts 11-3 Course 3 Additional Example 4 Continued Solve for b. 4 = 2 + b –2–2 Subtract 2 from both sides. 2 = b Write the equation of the line, using –2 for m and 2 for b. y = –2x + 2 Great job! You did it! What is the slope? What is the y-intercept? What does the graphed line look like?

  28. Using Slopes and Intercepts 11-3 y2 – y1 = x2 – x1 6 – 2 4 2 – 1 1 = Course 3 Try This: Example 4 Write the equation of the line that passes through (1, 2) and (2, 6) in slope-intercept form. Find the slope. = 4 The slope is 4. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b Substitute 1 for x, 2 for y, and 4 for m. 2 = 4(1) + b 2 = 4 + b Simplify.

  29. Using Slopes and Intercepts 11-3 Course 3 Try This: Example 4 Continued Solve for b. 2 = 4 + b –4–4 Subtract 4 from both sides. –2 = b Write the equation of the line, using 4 for m and –2 for b. You did it again! What is the slope? What is the y-intercept? What does the graphed line look like? y = 4x – 2

  30. Using Slopes and Intercepts 11-3 y = – x + 2 3 4 Course 3 Insert Lesson Title Here 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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