equations of lines in the coordinate plane
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Equations of Lines in the Coordinate Plane. Section 3.7 p.189. Graphing Linear Equations. Definitions : Cartesian Coordinate Plane – a graph X – axis – the horizontal axis of a coordinate plane Y – axis – the vertical axis of a coordinate plane. Graphing Linear Equations.

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graphing linear equations
Graphing Linear Equations
  • Definitions:
  • Cartesian Coordinate Plane – a graph
  • X – axis –
  • the horizontal axis of a coordinate plane
  • Y – axis –
  • the vertical axis of a coordinate plane
graphing linear equations1
Graphing Linear Equations
  • Definitions:
  • Origin –

where the two axes meet (0,0)

  • Ordered pair –
    • x and y values of a point on a graph
    • Also called a point of a set of coordinates
  • Quadrants – the four sections that the x and y axes divide the coordinate plane into – named I, II, III, and IV
coordinate plane
Coordinate Plane
  • Identify
    • Origin
    • Y-axis
    • X-axis
    • Quadrants I, II, III, and IV
rise up run out
“Rise Up Run Out”
  • Slope
    • “Steepness”
    • What are some examples where slope is a factor?

grade of a road, incline of wheelchair ramp, pitch of a roof, etc.

slope of a line
Slope of a Line
  • Slope
  • =
  • =
  • Pick any two points on a line to compute the slope
determine the slope of a line given the coordinates of two points on the line
Determine the slope of a line given the coordinates of two points on the line
  • Given A (-1,2) and B (4, -2)
  • Find the slope of line AB
find the slope of the segment below
Find the slope of the segment below
  • (5, 4) and (3, -1)
  • Slope =
  • m= =
slide13
Positive vs. negative slope
  • Positive slope- rises to the right
  • Negative slope- falls to the right
slope
Slope
  • Horizontal line
    • Slope = ∆y = 0 = 0

∆x ∆x

  • Vertical line
    • Slope = ∆y = ∆y = undefined

∆x 0

slide15
Given C (4, 0) and D (4, -2)
  • Find the slope of line CD
  • undefined
slope of a line1
Slope of a Line
  • Special cases:
  • x = 4
  • What will this slope be?
  • y = - 3
  • What will this slope be?
slope intercept f orm
Slope-Intercept Form
  • Given
  • What is the slope?
  • What are the coordinates of the y-intercept?
  • (0, -5)
point slope form
Point-Slope Form
  • = )
  • Given point A (3, 5) on the line with a slope of -1, find the equation of the line in point-slope form.
  • = )
  • Write the equation of this line in slope-intercept form.
  • =
slide20
What is the equation of a line in point-slope form passing through point A(-2,-1) and B(3, 5)?
  • First find the slope;
  • Then plug one of the points into the point-slope form of the line;
more practice
More Practice
  • What is the equation of a line in slope intercept form with slope of -2 and a y-intercept of (0, 5)?
  • In point-slope form?
  • y- 5 = -2(x-0)
  • What is the equation in point-slope form of the line through (-1, 5) with a slope of 2?
  • In slope-intercept form?
homework
Homework
  • P.194-195 #9-41 odd
  • Additional Practice
  • 13-2 Slope of a Line worksheet
3 8 slopes of parallel and perpendicular lines
3.8 Slopes of Parallel and Perpendicular Lines
  • Two non-vertical lines are parallel if and only if their slopes are equal.
  • (parallel lines have the same slope)
  • Two non-vertical lines are perpendicular if and only if the product of their slopes is -1
  • (slopes of perpendicular lines are negative reciprocals of each other)
  • m1 *m2 = -1 or m1= -1/m2
slide27
Are the two lines below parallel?
  • y= -3x +4 and y=-3x -10
  • y= 4x-10 and y=2x-10
  • y= x +5 and y = x +7
  • Are the two lines below perpendicular?
  • y= 4x – 2 and y= -x +5
  • y= -x +4 and y= x +4
  • y=x -10 and y= +5
slide28
Given a line through points (5,-1) and (-3, 3), find the slope of all lines
    • A. parallel to this one
    • B. perpendicular to this one
  • Slope = (-1 – 3)/ (5 – (-3)) = -4/8 = -1/2
  • A. slope = -1/2
  • B. slope = 2
are the two lines below perpendicular
Are the two lines below perpendicular?
  • (-4, 2) and (0, -4)
  • (-5, -3) and (4, 3)
homework1
Homework
  • p.201-203 #7-10, 15-18, 23, 25, 31, 33
  • 13-3 Parallel and Perpendicular Lines worksheet
  • 13-7 Writing Linear Equations worksheet #11-23 odd, 24-26 all
find the distance between points a and b
Find the distance between points A and B

A

B

Two points in a horizontal line

Distance = absolute value of the difference in the

x-coordinates

Distance=|-2 – 2| = 4 or |2 – (-2)| = 4

find the distance between points a and b1
Find the distance between points A and B

A

B

Two points in a vertical line

Distance = absolute value of the difference in the

y-coordinates

Distance=|-8 – 3| = 11 or |3 – (-8)| = 11

slide33
What about two points that do not lie on a horizontal or vertical line?
  • How can you find the distance between the points?
  • The distance between two points is equal to the length of the segment with those points as the endpoints
the distance formula
The Distance Formula
  • The distance between points (x1, y1) and (x2, y2) is given by:
  • d =
  • Find the distance between (0, 0) and (7, 24)
  • d =
  • d = 25
midpoint formula review
Midpoint Formula Review
  • Find the midpoint of the line segment with endpoints (4, 7) and (-2, 5)
  • (1, 6)
class work
Class work
  • 13-1 Distance Formula worksheet
  • 13-5 Midpoint Formula worksheet
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