1. Advanced Algebra 1

2. Slope-Intercept Form Point-Slope Form

3. Let’s try one… Given “m” (the slope remember!) = 2 And “b” (the y-intercept) = (0, 9) All you have to do is plug those values into y = mx + b The equation becomes… y = 2x + 9

4. Given m = 2/3, b = -12, Write the equation of a line in slope-intercept form. Y = mx + b Y = 2/3x – 12 ************************* One last example… Given m = -5, b = -1 Write the equation of a line in slope-intercept form. Y = mx + b Y = -5x - 1

5. GUIDED PRACTIE Write an equation of the line that has the given slope and y- intercept. 1. m = 3, b = 1 y = x + 1 3 ANSWER 2. m = –2, b = –4 y = –2x – 4 ANSWER 3. m = –, b = 3 4 7 2 y = – x + 3 4 7 2 ANSWER

6. 1) m = 3, b = -14 2) m = -½, b = 4 3) m = -3, b = -7 4) m = 1/2, b = 0 5) m = 2, b = 4 6) m = 0, b = -3 y = 3x - 14 y =-½x + 4 y =-3x - 7 y = ½x y =2x + 4 y = - 3

7. Write an equation of the line shown in slope- intercept form. m = ¾ b = (0,-2) y = ¾x - 2

8. True False

9. a) -4/3 b) -3/4 c) 4/3 d) -1/3

10. a) x = -5 b) y = 7 c) x = y d) x + y = 0

11. Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2. y – y 1 = m(x – x 1 ) y – 1 = -2(x – 4) Substitute 4 for x 1, 1 for y 1 and -2 for m. Write in slope-intercept form. y – 1 = -2x + 8 Add 1 to both sides y = -2x + 9

12. Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7. y – y 1 = m(x – x 1 ) y – 3 = 7[x – (-1)] y – 3 = 7(x + 1) Write in slope-intercept form y – 3 = 7x + 7 y = 7x + 10

13. y 2 – y 1 m =m = x 2 – x 1 4--4 = -1-3 8 –4 == –2 y 2 – y 1 = m(x – x 1 ) Use point-slope form. y + 4 = – 2(x – 3) Substitute for m, x 1, and y 1. y + 4 = – 2x + 6 Distributive property Write in slope-intercept form. y = – 2x + 2

14. 1) (-1, -6) and (2, 6) 2) (0, 5) and (3, 1) 3) (3, 5) and (6, 6) 4) (0, -7) and (4, 25) 5) (-1, 1) and (3, -3)

15. GUIDED PRACTICE for Examples 2 and 3 GUIDED PRACTICE 4. Write an equation of the line that passes through (–1, 6) and has a slope of 4. y = 4x + 10 5. Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1. y = 3x – 14 ANSWER

16. Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form SOLUTION The line passes through (x 1, y 1 ) = (5,–2) and (x 2, y 2 ) = (2, 10). Find its slope. y 2 – y 1 m =m = x 2 – x 1 10 – (–2) = 2 – 5 12 –3 == –4 y 2 – y 1 = m(x – x 1 ) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x 1, and y 1. y – 10 = – 4x + 8 Distributive property Write in slope-intercept form. y = – 4x + 18

17. 1) Which of the following equations passes through the points (2, 1) and (5, -2)? a. y = 3/7x + 5b. y = -x + 3 c.y = -x + 2d. y = -1/3x + 3

18. a) y = -3x – 3 b) y = -3x + 17 c) y = -3x + 11 d) y = -3x + 5

19. EXAMPLE 3 Write an equation in slope-intercept that is perpendicular to y = -4x + 2 and goes through the point (-2, 3) y – y 1 = m 2 (x – x 1 ) Use point-slope form. y – 3 = (x – (–2)) 1 4 Substitute for m 2, x 1, and y 1. y – 3 = (x +2) 1 4 Simplify. y – 3 = x + 1 4 1 2 Distributive property Write in slope-intercept form. Write equations of parallel or perpendicular lines

20. y = 3 (or any number) Lines that are horizontal have a slope of zero. They have “run” but no “rise”. The rise/run formula for slope always equals zero since rise = o. y = mx + b y = 0x + 3 y = 3 This equation also describes what is happening to the y-coordinates on the line. In this case, they are always 3.

21. x = -2 Lines that are vertical have no slope (it does not exist). They have “rise”, but no “run”. The rise/run formula for slope always has a zero denominator and is undefined. These lines are described by what is happening to their x-coordinates. In this example, the x- coordinates are always equal to -2.

22. a) x = -5 b) y = 7 c) x = y d) x + y = 0

23. a) Y = 2x + 3 b) Y – 2x = 4 c) 2x – y = 8 d) Y = -2x + 1

24.  The data shows a relationship between the number of years of college and salary earned. Plot this data and create a line of best fit. Remember to pick to two points and create a line in slope-intercept form.  (Scale for x: 0 to 8, Scale for y: 0 to 50 (Go by 5’s)) Years of college 32462.57.5715.54 Salary (in $1000) 15202247191832103028

25.  I selected the points (2.5, 19) and (7, 32) on that line to determine the equation of the line.  Which ones did you pick?

26. Step 4: Use point-slope form to make an equation. Did you get a similar slope or y-intercept?

27.  Prediction equation is y = 2.9x + 11.7  For example, we can predict that with five years of college education, their salary might be $26,200.  What will 8 years of college get her salary to be?  About $33,900

28.  Step 1: Graph the data points. Height (inches) 60626466687072 Weight (pounds) 105111123130139149158 Draw a line that appears to be most representative of the data. That ’ s your line of best fit.

30. Slope-intercept form Substitute values into form. Multiply 4.8 by 62 to simplify. Subtract 297.6 from both sides. Prediction equation

31.  Step 1: Graph the data points. Experience (weeks) 4781635296710 Typing Speed (wpm) 334546204030382252444255 Scale x: 0 to 10 Scale y: 0 to 60 (Go by 5’s)

33. Now plug in 11 for x so that we can predict the speed of typing after 11 weeks. So there speed is 61.8 words per minute