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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.

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

• 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

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

### 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