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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Equations of Lines in the Coordinate Plane

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Equations of lines in the coordinate plane

Equations of Lines in the Coordinate Plane

Section 3.7 p.189


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= =


Equations of lines in the coordinate plane

  • 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


Equations of lines in the coordinate plane

  • 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)


Graph y x 5

Graph y = x -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.

  • =


Equations of lines in the coordinate plane

  • 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


Equations of lines in the coordinate plane

  • How do you think the slopes of parallel lines compare?

  • What about perpendicular lines?


Slopes of parallel lines gsp

Slopes of Parallel Lines (GSP)


Slopes of perpendicular lines gsp

Slopes of Perpendicular Lines (GSP)


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


Equations of lines in the coordinate plane

  • 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


Equations of lines in the coordinate plane

  • 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


Equations of lines in the coordinate plane

  • 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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