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Sect P-4

Sect P-4. Lines in the Plane. Slope of a line. If the line is vertical , the slope is “ undefined ”. Find the slope…. Passes through (-1,2) and (4,2) . Point-Slope Form of the Line. Find the Point-Slope Form. Line passes through (-3,-4) with a slope of 2. Slope-Intercept Form.

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Sect P-4

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  1. Sect P-4 Lines in the Plane

  2. Slope of a line If the line is vertical, the slope is “undefined”

  3. Find the slope… • Passes through (-1,2) and (4,2)

  4. Point-Slope Form of the Line

  5. Find the Point-Slope Form • Line passes through (-3,-4) with a slope of 2

  6. Slope-Intercept Form • Y-intercept: the point where the line crosses (intersects) the y-axis • It will always cross at x=0. • y=mx + b m = slope of line b = the y value of the y-intercept of line… y-intercept is (0,b)

  7. Using the Slope-Intercept Form • Write the equation of the line with slope 3 that passes through (-1,6)

  8. Forms of the Equation of Lines • Standard Form: • Slope-Intercept: • Point-Slope: • Vertical Line: • Horizontal Line:

  9. Graphing Linear Equations • The “graph” is all pairs (x,y) that are solutions to the equation. • (2,1) is “one” solution to 2x + 3y = 8 • Substituting x=2 and y = 1 into the equation will give the answer 8. • There are infinitely many points on the graph.

  10. Graphing Linear Equations • Using Calculator • Solve the equation for y= • Enter into y= screen on calculator • Hit “graph” • Note: the graph window may need to be changed to view the parts needed.

  11. Parallel Lines • What do graphs of y = mx + b and y = mx + c have in common? How are they different?

  12. Perpendicular Lines • Graph y = 2x and y = - (1/2)x in a “square” viewing window. • Estimate the angle between the lines. • What can you say about the “slopes” of the two lines?

  13. Definitions… • Two non-vertical lines are “parallel” if and only if they have the same slope. • Two non-vertical lines are “perpendicular” if and only if their slopes m1 and m2 are “opposite reciprocals” of each other.

  14. Homework… P. 35 • Quick Review … 2,6,8 • Exercises …6, 10, 14, 18, 24, 34 (using calculator on 34 only)

  15. Find the Equation of Perpendicular Line • Given a line 4x + y = 3 • Find the equation of the perpendicular line that passes through (2,-3)

  16. Applying Linear Equations • Camelot Apartments purchased a $50,000 building and depreciates it (for tax purposes) $2000 per year over a 25 year period. • Write the equation showing the value of the building (for tax purposes) in terms of years after the purchase. • In how many years will the value be $24,500?

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