1 / 36

# Equations of Lines in the Coordinate Plane - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Equations of Lines in the Coordinate Plane' - gloria-barber

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Equations of Lines in the Coordinate Plane

Section 3.7 p.189

• Definitions:

• Cartesian Coordinate Plane – a graph

• X – axis –

• the horizontal axis of a coordinate plane

• Y – axis –

• the vertical axis of a coordinate plane

• 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

• Identify

• Origin

• Y-axis

• X-axis

• Quadrants I, II, III, and IV

• 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

• =

• =

• 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

• Given A (-1,2) and B (4, -2)

• Find the slope of line AB

Find the slope of the segment below points on the line

• (5, 4) and (3, -1)

• Slope =

• m= =

• Positive points on the line vs. negative slope

• Positive slope- rises to the right

• Negative slope- falls to the right

Slope points on the line

• Horizontal line

• Slope = ∆y = 0 = 0

∆x ∆x

• Vertical line

• Slope = ∆y = ∆y = undefined

∆x 0

Slope of a Line points on the line

• Special cases:

• x = 4

• What will this slope be?

• y = - 3

• What will this slope be?

Slope-Intercept points on the lineForm

• Given

• What is the slope?

• What are the coordinates of the y-intercept?

• (0, -5)

Graph y = points on the linex -5

Point-Slope Form points on the line

• = )

• 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.

• =

More Practice through point A(-2,-1) and B(3, 5)?

• 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 through point A(-2,-1) and B(3, 5)?

• P.194-195 #9-41 odd

• 13-2 Slope of a Line worksheet

Slopes of Parallel Lines (GSP) through point A(-2,-1) and B(3, 5)?

Slopes of Perpendicular Lines (GSP) through point A(-2,-1) and B(3, 5)?

3.8 Slopes of Parallel and Perpendicular Lines through point A(-2,-1) and B(3, 5)?

• 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

• Are the two lines below parallel? through point A(-2,-1) and B(3, 5)?

• 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

Are the two lines below perpendicular? slope of all lines

• (-4, 2) and (0, -4)

• (-5, -3) and (4, 3)

Homework slope of all lines

• 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 slope of all lines

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 B slope of all lines

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

The Distance Formula vertical line?

• 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 vertical line?

• Find the midpoint of the line segment with endpoints (4, 7) and (-2, 5)

• (1, 6)

Class work vertical line?

• 13-1 Distance Formula worksheet

• 13-5 Midpoint Formula worksheet