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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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Systems of Linear Equations Method 1: Using a Graph to Solve Method 2 : Solve by Substitution Method 3 : Solve by Linear Combination / Elimination.

Systems of Linear Equations Method 1: Using a Graph to Solve Method 2 : Solve by Substitution Method 3 : Solve by Linear Combination / Elimination.

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