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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

Sect P-4

Lines in the Plane

slope of a line
Slope of a line

If the line is vertical,

the slope is “undefined”

find the slope
Find the slope…
  • Passes through (-1,2) and (4,2)
find the point slope form
Find the Point-Slope Form
  • Line passes through (-3,-4) with a slope of 2
slope intercept form
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
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
Forms of the Equation of Lines
  • Standard Form:
  • Slope-Intercept:
  • Point-Slope:
  • Vertical Line:
  • Horizontal Line:
graphing linear equations
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 equations1
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
Parallel Lines
  • What do graphs of y = mx + b and

y = mx + c have in common?

How are they different?

perpendicular lines
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
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
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
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
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?