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Understanding Slope and Linear Equations in Plane Geometry

Dive into the fundamentals of slope and linear equations in this comprehensive guide. Learn how to calculate the slope using different points, write linear equations in point-slope form, and understand the implications of parallel and perpendicular lines. Explore real-world applications with examples like sales predictions. Additionally, practice your skills with exercises that encompass slope calculations, linear extrapolation, and graphing techniques. Equip yourself with the knowledge to tackle problems involving slopes and linear models confidently.

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Understanding Slope and Linear Equations in Plane Geometry

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  1. Do Now 1.If f(x) = │(x² – 50)│, what is the value of f(-5) ? A. 75 B. 25 C. 0 D. -25 E. -75 2.( √2 - √3 )² = A. 5 - 2√6 B. 5 - √6 C. 1 - 2√6 D. 1 - √2 E. 1 3.230 + 230 + 230 + 230 = A. 8120B. 830C. 232D. 230E. 226

  2. P.3 Lines in the Plane SWBAT 1. Find the slope of a line. 2. Write linear equations given points on lines and their slopes. 3. Use slope-intercept forms of linear equations to graph lines. 4. Use slope to identify parallel and perpendicular lines.

  3. The slope of a line • Slope: rise over run, the change in y over the change in x

  4. The slope of a line • Finding slope given 2 points: • 1. (-2, 0) and (3, 1) • 2. (-1, 2) and (2, 2) • 3. (3, 4) and (3, 1)

  5. The point-slope form of a line • Point-slope form: y – y1 = m(x – x1) • Find an equation of the line that passes through the point (1, -2) and has a slope of 3. • Find an equation of the line that passes through (2, -3) and (4, 5).

  6. Using point-slope to create linear models • During 1997, Barnes and Noble’s net sales were $2.8 billion, and in 1998 net sales were $3.0 billion. • 1. Write a linear equation giving the net sales y in terms of the year x. • 2. Use the equation to estimate the net sales during 2000.

  7. Linear extrapolation: an approximation in which the estimated point lies outside of the given points • Linear interpolation: the estimated point lies between the two given points

  8. Sketching graphs of lines • Slope-intercept form: y = mx + b • Better suited to graph linear equations

  9. Sketching graphs of lines • Determine the slope and y-intercept of each linear equation and describe its graph. • 1. x + y = 2 • 2. y = 2

  10. Parallel Lines • Parallel lines: have slopes that are equal • Find the slope-intercept form of the equation of the line that passes through the point (2, -1) and is parallel to the line 2x – 3y = 5.

  11. Perpendicular Lines • Perpendicular lines: have slopes that are negative reciprocals • Find an equation of the line that passes through the point (2, -1) and is perpendicular to the line 2x – 3y = 5.

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