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Geometry

Geometry. 13.7 Writing Linear Equations. Slope Intercept Form. Write an equation of the line whose slope m is -2 and whose y-intercept b is 5. m = -2 b = 5 y = m x + b y = -2 x + 5. Complete exercises #1-3 in Part I and check below. 1. y = 2x - 1. 2. y = -½x + 4.

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Geometry

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  1. Geometry 13.7 Writing Linear Equations

  2. Slope Intercept Form Write an equation of the line whose slope m is -2 and whose y-intercept b is 5. m = -2 b = 5 y = mx + b y = -2x + 5 Complete exercises #1-3 in Part I and check below. 1. y = 2x - 1 2. y = -½x + 4 3. y = -2/3x + 1/3

  3. Point Slope Form (PS) Today we will use this formula to find the equation of a line when you are only given either: the slope and one point on the line. two points on the line.

  4. Part III #1: Given point and slope. Step 1: Use PS Form Using (2, 5) and m = 4 • (2, 5) Step 2: Simplify to SI Form • y - 5 = 4x - 8 (0,-3) +5 +5 y = 4x - 3

  5. Part III- Do #2 and #3: Given point and slope. 2. Using (6, -6) and m = -2/3 3. Using (-4, 0) and m = -½ -6 -6 y = -2/3x - 2 y = -½x - 2

  6. Part IV #1: Given 2 points. (1,2) and (4,7) Step 1: Compute slope You can check with other point: 7 = 5/3(4) + 1/3 Step 2: Use PS Form 7 = 20/3 + 1/3 Using (1, 2) 7 = 21/3 check! 7 = 7 Step 3: Simplify to SI Form +2 y = 5/3x + 1/3

  7. Now you try #2 and #3. Write the equation of the line through the two given points. 2. (2, 5) and (1, -2) m = 7 PS: y - 5 = 7(x – 2) or y + 2 = 7(x - 1) SI: y = 7x - 9 3. (-2, -4) and (-3, -1) m = -3 PS: y + 4 = -3(x + 2) or y + 1 = -3(x + 3) SI: y = -3x - 10

  8. Horizontal Lines y Horizontal lines are all parallel to each other and perpendicular to all vertical lines. y = 5 y = 3 x y = -2 y = -6 Horizontal lines all have a slope of 0.

  9. Vertical Lines y x = 3 x = 5 x = -6 x = -2 Vertical lines are all parallel to each other and perpendicular to all horizontal lines. x Vertical lines all have a slope that is UNDEFINED.

  10. Part VI #1: Point and parallel or perpendicular line. (9,-2) and parallel to y = x + 3 Use (9,-2) and the same slope of m = 1 Use PS form: y + 2 = 1(x – 9) y + 2 = x - 9 y = x - 11 Check: -2 = 9 - 11 -2 = -2 check!

  11. Part VI #3: Point and parallel or perpendicular line. (-6,1) and perpendicular to y = -3/2x - 1 Use (-6,1) and the opposite reciprocal slope of m = 2/3 Use PS form: y - 1 = 2/3(x + 6) y - 1 = 2/3x + 4 y = 2/3x + 5 Check: 1 = 2/3(-6) + 5 1 = -4 + 5 1 = 1 check!

  12. Part VI #2: (-4,1) and horizontal line y = 1 Part VI #4: (-3,-5) and vertical line x = -3

  13. Part VI #5: (8,7) and parallel to x = -2 x = 8 All vertical lines are parallel Part VI #6: (2,2) and perpendicular to y = 3 x = 2 A vertical line is perpendicular to a horizontal line

  14. Homework pg. 555 #1-16 Even #17-33 Odd Reminder to Mr. Willis Print out Test Averages from the year Sometime late do the alg. 2 read. test

  15. Homework HW is evens b/c we did odds w/sub Reminder to Mr. Willis Print out Test Averages from the year Sometime late do the alg. 2 read. test

  16. Given x and y intercepts: 1. x-int: 2 y-int: -3 (2,0) (0,-3) Notice that the slope is rise 3 (-3) ● - or (2,0) run 2 2 ● y-int (0,-3) or opposite x-int. The y intercept (b) of -3 is given 3 The equation in slope intercept form is y = x - 3 2

  17. Given Intercepts To write the equation in slope-intercept form use the pattern : y-intercept + y-intercept y = x x-intercept b slope m Complete exercises #2-3 in Part II and check below. 2. y = 3/4x + 3 3. y = -7/3x - 7

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