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Understanding Slope-Intercept and Point-Slope Forms in Linear Equations

This guide explores the concepts of slope-intercept form and point-slope form of linear equations. It details the definitions where 'm' represents the slope and 'b' the y-intercept. Learn how to derive equations from two given points and how to manipulate point-slope form to reach slope-intercept form. Utilizing examples, such as finding equations for lines based on specific slopes and intercepts, this resource will strengthen your understanding of graphing linear equations and applying these forms in practice.

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Understanding Slope-Intercept and Point-Slope Forms in Linear Equations

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  1. Point-Slope Form

  2. What we Know so far…. Slope Intercept Form Where m is the slope and b is the intercept

  3. What we Know so far…. Slope Where two points are given as (x1,y1) and (x2,y2)

  4. The New Stuff… Write equations Slope-intercept form is: Where m is the slope and b is the y-intercept Example: Find the equation of the line with slope -2 and y-intercept 8 y = -2x + 8 Easy if I know the y-intercept… but if I don’t?

  5. The New Stuff… Point- Slope Form Point- Slope form is: Where m is the slope and (x1,y1) is the given point that the line goes through

  6. The New Stuff… Point- Slope Form Point- Slope form is: Where does this equation come from?

  7. Using Point-Slope Form to graph 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 Slope is Point is (2,3)

  8. Manipulate Point-Slope Form to Slope-Intercept form Simplify

  9. Using Point-Slope Form to graph 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 Slope is Point is (4,-3)

  10. Manipulate Point-Slope Form to Slope-Intercept form

  11. Your turn

  12. Homework Pg. 304 #2 to 8 even Write slope and point Plot graph Write equation in slope intercept form

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