Equations of Lines in the Coordinate Plane

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# 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.

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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
• 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
• Identify
• Origin
• Y-axis
• X-axis
• Quadrants I, II, III, and IV
“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
• =
• =
• 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
• (5, 4) and (3, -1)
• Slope =
• m= =
Positive vs. negative slope
• Positive slope- rises to the right
• Negative slope- falls to the right
Slope
• Horizontal line
• Slope = ∆y = 0 = 0

∆x ∆x

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

∆x 0

Given C (4, 0) and D (4, -2)
• Find the slope of line CD
• undefined
Slope of a Line
• Special cases:
• x = 4
• What will this slope be?
• y = - 3
• What will this slope be?
Slope-Intercept Form
• Given
• What is the slope?
• What are the coordinates of the y-intercept?
• (0, -5)
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.
• =
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
• 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
• P.194-195 #9-41 odd
• 13-2 Slope of a Line worksheet
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
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
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?
• (-4, 2) and (0, -4)
• (-5, -3) and (4, 3)
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

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

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

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 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
• Find the midpoint of the line segment with endpoints (4, 7) and (-2, 5)
• (1, 6)
Class work
• 13-1 Distance Formula worksheet
• 13-5 Midpoint Formula worksheet