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Understanding and Writing Linear Equations in Slope-Intercept Form

This guide covers writing equations of lines in slope-intercept form and point-slope form, using given slopes and points. Learn how to derive equations from points, calculate slopes, and convert between forms. Examples illustrate the process, including how to find slope from two points and how to express the equation in both forms. This resource is ideal for students mastering linear equations, seeking clarity in the form and function of linear equations, and understanding the significance of slopes and y-intercepts.

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Understanding and Writing Linear Equations in Slope-Intercept Form

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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. EVERY ONE GET A COMMUNICATOR: WITH A BLANK SIDE!!

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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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!!

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

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