Sect P-4

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# Sect P-4 - PowerPoint PPT Presentation

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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Presentation Transcript

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

Using the Slope-Intercept Form
• Write the equation of the line with slope 3 that passes through (-1,6)
Forms of the Equation of Lines
• Standard Form:
• Slope-Intercept:
• Point-Slope:
• Vertical Line:
• Horizontal Line:
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.
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.
Parallel Lines
• What do graphs of y = mx + b and

y = mx + c have in common?

How are they different?

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?
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.
Homework… P. 35
• Quick Review … 2,6,8
• Exercises …6, 10, 14, 18, 24, 34 (using calculator on 34 only)
Find the Equation of Perpendicular Line
• Given a line 4x + y = 3
• Find the equation of the perpendicular line that passes through (2,-3)
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?