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Chapter 5 Reivew

Chapter 5 Reivew. Test Topics. 1.Given slope ( m ) and y -intercept ( b ) create the equation in slope-intercept form. 2. Look at a graph and write an equation of a line in slope-intercept form. 3. Know how to plug into point-slope form. 4. Find the slope between two points.

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Chapter 5 Reivew

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  1. Chapter 5 Reivew

  2. Test Topics 1.Given slope (m) and y-intercept (b) create the equation in slope-intercept form. 2. Look at a graph and write an equation of a line in slope-intercept form. 3. Know how to plug into point-slope form. 4. Find the slope between two points. 5. Write an equation of a line that passes through two points. 6. Find an equation of a line that is parallel to an equation given and also given a random point. 7. Find an equation of a line given a slope and a random point. 8. Decide which two lines are parallel. 9. Convert an equation into standard form. 10. Write an equation of a horizontal (y = #) or vertical line (x = #). 11. Decide which two lines are perpendicular. 12. Look at an equation of a line and find the slope of that line.

  3. Various Forms of an Equation of a Line. Slope-Intercept Form Standard Form Point-Slope Form

  4. Review 5.1-5.2

  5. Write the equation of a line after you are given the slope and y-intercept… Let’s try one… Given “m” (the slope remember!) = 2 And “b” (the y-intercept) = +9 All you have to do is plug those values into y = mx + b The equation becomes… y = 2x + 9

  6. Let’s do a couple more to make sure you are expert at this. 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

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

  8. Given the slope and y-intercept, write the equation of a line in slope-intercept form. 1) m = 3, b = -14 2) m = -½, b = 4 3) m = -3, b = -7 4) m = 1/2 , b = 0 • m= 2, b = 4 • m = 0, b = -3 y = 3x - 14 y =-½x + 4 y =-3x - 7 y = ½x y =2x + 4 y = - 3

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

  10. 3) The slope of this line is 3/2? True False

  11. 5) Which is the slope of the line through (-2, 3) and (4, -5)? • -4/3 • -3/4 • 4/3 • -1/3

  12. 8) Which is the equation of a line whose slope is undefined? • x = -5 • y = 7 • x = y • x + y = 0

  13. Review 5.3-5.4 Point-Slope Form Standard Form

  14. Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2. y – y1 = m(x – x1) y– 1 = -2(x – 4)Substitute 4 for x1, 1 for y1 and -2 for m. Write in slope-intercept form. y – 1 = -2x + 8Add 1 to both sides y = -2x + 9

  15. Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7. y – y1 = m(x – x1) y – 3 = 7[x – (-1)] y – 3 = 7(x + 1) Write in slope-interceptform y – 3 = 7x + 7 y = 7x + 10

  16. 8 –4 4--4 y2 – y1 = m= = = –2 x2 – x1 -1-3 Write the equation of a line in slope-intercept form that passes through points (3, -4) and (-1, 4). y2– y1=m(x –x1) Use point-slope form. y + 4=–2(x –3) Substitute for m, x1, and y1. y + 4= – 2x + 6 Distributive property y = – 2x + 2 Write in slope-intercept form.

  17. Write the equation of the line in slope-intercept form that passes through each pair of points. • (-1, -6) and (2, 6) • (0, 5) and (3, 1) • (3, 5) and (6, 6) • (0, -7) and (4, 25) • (-1, 1) and (3, -3)

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

  19. 12 –3 10 – (–2) y2 – y1 = m= = = –4 x2 – x1 2 –5 Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form SOLUTION The line passes through (x1, y1) = (5,–2) and (x2, y2) = (2, 10). Find its slope. y2– y1=m(x –x1) Use point-slope form. y–10=–4(x –2) Substitute for m, x1, and y1. y–10 = – 4x + 8 Distributive property y = – 4x + 18 Write in slope-intercept form.

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

  21. 9) Which is the equation of a line that passes through (2, 5) and has slope -3? • y = -3x – 3 • y = -3x + 17 • y = -3x + 11 • y = -3x + 5

  22. 4 2 9–5 y2 – y1 = m= = =2 x2 – x1 1–-1 Write equation of the line in standard form that passes through (-1,5) and (1,9) y–9=2(x –1) y–9=2x - 2 y=2x + 7 -2x -2x -2x + y = 7 2x -y = -7

  23. Write equation of the line in standard form that has a slope of ½ and passes through (4,-5). y + 5= ½(x –4) y + 5= ½x - 2 y= ½x - 7 Multiply everything by 2 to get rid of the fraction 2y=x- 14 -x -x -x + 2y = -14 x- 2y = 14

  24. Write equation of the line in standard form that is parallel to y=⅔x-8 and passes through (6,4) m = ⅔ y–4= ⅔(x –6) y–4 = ⅔x- 4 y= ⅔x Multiply everything by 3 to get rid of the fraction 3y= 2x -2x -2x -2x + 3y = 0 2x - 3y = 0

  25. EXAMPLE 2 Write an equation in standard form of the line that passes through (5, 4) and has a slope of –3. SOLUTION y –y1=m(x –x1) Use point-slope form. y –4=–3(x –5) Substitute for m,x1, and y1. y – 4 = –3x + 15 Distributive property y= –3x + 19 Write in slope-intercept form. +3x +3x 3x + y= 19

  26. Review 5.6 Parallel vs. Perpendicular Lines

  27. 1 1 1 b. A line perpendicular to a line with slope m1 = –4 has a slope of m2 = – = . Use point-slope form with (x1, y1) = (–2, 3) 4 2 4 1 m1 y –3= (x – (–2)) 1 y – 3 = (x +2) 4 1 4 y – 3 = x + EXAMPLE 3 Write equations of parallel or perpendicular lines y –y1=m2(x –x1) Use point-slope form. Substitute for m2, x1, andy1. Simplify. Distributive property Write in slope-intercept form.

  28. Horizontal Lines 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.

  29. Vertical Lines 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.

  30. 8) Which is the equation of a line whose slope is undefined? • x = -5 • y = 7 • x = y • x + y = 0

  31. Which of these equations represents a line parallel to the line 2x + y = 6? • Y = 2x + 3 • Y – 2x = 4 • 2x – y = 8 • Y = -2x + 1

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