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First let’s review 5.1

Learn how to write a line equation using slope-intercept and point-slope forms with various examples and step-by-step instructions. Understand how to calculate the slope, select the form of the equation, and substitute the values for precise results.

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First let’s review 5.1

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  1. First let’s review 5.1 Write the equation in slope-intercept form, given m = 3 ang b = (0,-2) Example m = 3, b = (0,-2) y = mx + b y = __ x + ___

  2. Write the equation of the line in slope-intercept form. m = 3/2 b = (0,1) y = mx + b

  3. Given this equation, what is the slope and y-intercept? +2x +2x 3y = 2x + 15 3 3 3 m = 2/3 b = (0,5)

  4. Review 5.2 Point-Slope Form

  5. Write the equation of the line in point-slope form. m = -1/3 (0,3) Or you can use any point (3,2)

  6. Given (2,3) and slope = -2, write the equation in SLOPE-INTERCEPT This is the equation of the line in point-slope form!! Now leave your answer in slope- intercept form. +3 +3

  7. Given (-8,4) and slope = -3/2, write the equation in SLOPE-INTERCEPT This is the equation of the line in point-slope form!! Now leave your answer in slope- intercept form. +4 +4

  8. 5.3 Writing equations of a line given two points

  9. Forms of a linear equation Slope-intercept Form y = mx + b Point-Slope Form y – y1 = m(x – x1)

  10. If given two points, (x1 , y1) and (x2 , y2) First, find the slope using the slope formula. Example contains (5, –8) and (2, 7) m = 15 –3 m = –5 m = 7 – -8 2 – 5

  11. If given two points, Then use the slope and EITHER point to work like the previous example. y – y1 = m(x – x1) y – 7 = – 5(x – 2) y – 7 = –5x + 10 m = –5, contains (5, –8) and (2, 7) y = –5x + 17

  12. Writing an Equation Given Two Points 1. Calculate the slope of the line. 2. Select the form of the equation. a. Slope-intercept form b. Point-slope form 3. Substitute and/or solve for the selected form.

  13. Writing an Equation Given Two Points Given the two ordered pairs, write the equation of the line in point-slope form. Calculate the slope. or

  14. Writing an Equation Given Two Points in point-slope form: Point-slope form

  15. Same example: Writing an Equation Given Two Points in slope-intercept form. Start by using point-slope form:

  16. 2.) Writing an Equation Given Two Points in slope-intercept form. (-5,7) (2,-7) Start by using point-slope form: + 7 + 7 - 7 - 7

  17. 3.) Writing an Equation Given Two Points in slope-intercept form. (2,0) (-2,6) Start by using point-slope form: + 3 + 3

  18. 4.) Writing an Equation Given Two Points in slope-intercept form. (10,-5) (8,4) Start by using point-slope form: - 5 - 5 - 7 - 7

  19. 5.) Writing an Equation Given Two Points in slope-intercept form. (6,5) (-3,5) Start by using point-slope form: + 5 + 5 + 5 + 5 Horizontal line

  20. 6.) Writing an Equation Given Two Points in slope-intercept form. (-2,-4) (-4,8) Start by using point-slope form: + 7 + 7 - 7 - 7

  21. 7.) Writing an Equation Given Two Points in slope-intercept form. (-6,6) (9,1) Start by using point-slope form: + 7 + 7 - 7 - 7

  22. NOW WHAT IF I GAVE YOU A GRAPH, TELL ME THE EQUATION OF THE LINE: WHAT’S THE MAJOR DIFFERENCE BETWEEN THESE TWO GRAPHS: So creating an equation using slope-intercept form would NOT work!!! The one on the right does not have a CLEAN y-intercept!!

  23. Create the equation of the line using two points on the line: (-3,4) (5,8)

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