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Sect P-4 Lines in the Plane

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

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

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Point-Slope Form of the Line

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

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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)

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

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

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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.

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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.

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

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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?

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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.

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

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

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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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Determining if Lines are Parallel or Perpendicular Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals (assume no vertical.

Determining if Lines are Parallel or Perpendicular Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals (assume no vertical.

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