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Understanding Equations of Lines: Slope-Intercept, General Form, & More

Learn about the equation of a line in various forms - slope-intercept, general form, slope-point form. Understand slope calculation and different line scenarios. Practice problems provided for better understanding.

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Understanding Equations of Lines: Slope-Intercept, General Form, & More

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  1. Aim: What is the equation of a line? Do Now: Find the slope of the line 8x + 5y = 20 x + 4 This is the slope – intercept form y = mx + b HW: Handout

  2. 8x + 5y = 20 is the called general form We use the notation Ax + By + C = 0 for general form of a line We can change the general form to slope-intercept form by solving for y , where is the slope What is the slope formula?

  3. If we cross-multiply This is called point-slope form To write the equation of a line if the slope and one point are known, just plug in the coordinates of the point and slope into = )

  4. Summary of the equation of a line I. slope-intercept form y = mx + b II. General form Ax + By + C = 0 III. Slope-point form )

  5. Things to remember If two lines are // then their slopes are equal If two lines are perpendicular then their slopes are negative reciprocal Horizontal line whose slope is 0 Vertical line whose slope is undefined

  6. Drill Find if A(1,2) and B(-1,-3) Find m of the line // to if A(1,-2) B(2,1) Write an equation of the vertical and horizontal line through (2,3) Write an equation of the line through (1,1) with m = 3 Write an equation of the line with m = -2 y-intercept = -1 Write an equation of the line through the points (3,1) and (-5,2)

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