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Mastering Lines: Slope Equations & Applications

Dive into the world of slopes, equations of lines, parallel & perpendicular lines, and their real-world applications. Learn the definitions, forms, and properties to ace this chapter effortlessly. Practice problems and detailed explanations included. Explore now!

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Mastering Lines: Slope Equations & Applications

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  1. Section P.4…slope, forms of equations of lines, parallel and perpendicular lines, + applications! We’re half way through this fantabulous chapter 

  2. Definition: Slope of a Line The slope of the nonvertical line through the points (x , y ) and (x , y ) is 1 1 2 2 y – y y 2 1 m = = x x – x 2 1 If the line is vertical, then x = x , and the slope is undefined. 1 2

  3. Forms of Equations of Lines Ax + By + C = 0 General Form: (A and B not both zero) y = mx + b Slope-Intercept Form: y – y = m(x – x ) Point-Slope Form: 1 1 x = a Vertical Line: y = b Horizontal Line:

  4. Guided Practice Find the slope of the line through the pair of points. (–1, 2) and (4, –2) (–9, –3) and (9, 25) 4 14 – m = m = 5 9

  5. Guided Practice Find the value of x or y so that the line through the pair of points has the given slope. (–2, 7) and (x, –2), m = 3 Equation for slope: x = –5

  6. Guided Practice Find the value of x or y so that the line through the pair of points has the given slope. (1, 6) and (–3, y), m = –2/3 Equation for slope: 26 y = 3

  7. Guided Practice Find the equation of the line through (–3, –4) with slope 2.  Use point-slope form  we love it!!! Rewrite in slope-intercept form: y = 2x + 2

  8. Guided Practice: Find a general form equation for the line through the pair of points (–3, –8) and (4, –1). First, find slope: Next, point-slope form: Re-write to general form: x – y – 5 = 0

  9. Guided Practice: Find the x- and y-intercepts of the following equation using your grapher: 436x + 9y = 1298 Solve for y: Graph window??? Calculate answers:

  10. More guided practice! Find the value of x and the value of y for which (x, 14) and (18, y) are points on the graph. 3x – 2y = 14 Plug in first point: Plug in second point: Complete points: (14, 14) and (18, 20)

  11. Parallel and Perpendicular Lines 1. Two nonvertical lines are parallel if and only if their slopes are equal. 2. Two non-vertical lines are perpendicular if and only if (iff) their slopes m and m are opposite reciprocals. That is, iff 1 2 1 m = 1 m 2

  12. Find an equation for the line passing through the point that is parallel to the given line and an equation through the given point that is perpendicular to the given line. (–2, 3) y = –2x + 4 Parallel Line Perpendicular Line Point: Slope: Point: Slope: Point-Slope Form: Point-Slope Form:

  13. Guided Practice: A corporation purchased a $50,000 building and depreciates it $2000 per year over a 25-year period. 1. Write a linear equation giving the value of y of the building in terms of the years x after the purchase. y = –2000x + 50,000 2. In how many years will the value of the building be $24,500? • Solve this three ways – algebraically, graphically, and using a table!

  14. Whiteboard Practice: Determine a and b so that the figure PROC is a parallelogram. R(a,b) O(8,5) P(1,0) C(6,0)

  15. Whiteboard Practice: Find the equation of the line through the points (4, 2) and (–3, 1). Write your answer in slope- intercept form. 1 10 y = x + 7 7 Homework: p. 40-43 3-25 odd, 41, 43, 55, 57 (fyi– next quiz after P5)

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