Chapter 4Chapter 4 – Coordinate – Coordinate Geometry:Geometry:

The Straight LineThe Straight Line James Kim

Michael Chang

Math 10

Block : D

Table of ContentsTable of Contents

4.1 – Using an Equation to Draw Graph

4.2 – The Slope of a Line

4.3 – The Equation of a Line :Part 1

4.4 – The Equation of a Line :Part 2

4.5 – Interpreting the Equation (Ax+By+C=0)

4.1 4.1 - Using an Equation - Using an Equation to Draw a Graphto Draw a Graph

Equation of a Line Property

The coordinates of every point on the line satisfy the equation of the line

Every point whose coordinates satisfy the equation of the line is on the line

4.14.1 - Using an Equation - Using an Equationto Draw a Graphto Draw a Graph

A basic equation

y=mx+b

m equals slopeb equals y-intercept

4.1 4.1 - Using an Equation - Using an Equation to Draw a Graphto Draw a Graph

Example (Using a calculator) Equation/ Y=2X+3

1. On a TI-83 Graphic calculator, go to Y= and type 2X+3 for Y1

2. Press window, and type numbers. (X min=-10, X max=10, X sc1=1, Y min=-10, Y max=10, Y sc1=1 X res=1)3. Press graph

You would get this on your graph -

4.1 4.1 - Using an Equation- Using an Equationto Draw a Graphto Draw a Graph

Example (No calculator) Equation/ Y=2X+3

1. You solve for Y, when X equals 1, 2, 3. You would get 5, 7, 9 for Y.

2. You draw zooms on the grid - - -

3. You draw line through the zooms - -

4.2 4.2 - The Slope of a Line- The Slope of a Line

Constant Slope Property The Constant Slope Property allows us to define the slope of a

line to be the slope of any segment of the line The Constant Slope Property is used to draw a line passing

through a given point with a given slope If the slope of two lines are equal, the lines are parallel Conversely, if two non-vertical lines are parallel. Their slopes

are equal. If the slopes of two lines are negative reciprocals, the lines are

perpendicular Conversely, if two lines are perpendicular, their slopes are

negative reciprocals

4.2 4.2 - The Slope of a Line- The Slope of a Line

Example For this graph, the coordinates

are

given, which are (1,-1) and (-2,3)

So the slope of this line segment is

M = (3-(-1)) / (-2-1)

The slope for this line is 4/-3

4.34.3 - - The Equation of a Line:The Equation of a Line:Part 1Part 1

The graph of the equation y = mx+b is a straight line with slope m and y-intercept b

Draw a graph with equation y=mx+b.

4.34.3 – The Equation of a Line – The Equation of a Line Part 1Part 1

Example

Equation y=4x-3

The slope is 4 and y intercept is –3

In calculator, go to Y=, and put Y1= 4x-3 - -

Then, press graph button and you will get - -

4.44.4 - The Equation of a Line: - The Equation of a Line:Part 1Part 1

Ax + By + C = 0

Standard form of the equation of a line

Collinear – Coordinates in the same straight

line

4.44.4 - The Equation of a Line: - The Equation of a Line:Part 1 Part 1

4 Cases of solving the Equation of a line4 Cases of solving the Equation of a line

Case 1 : Given two coordinates

Case 2 : Given slope and y-intercept

Case 3 : One coordinate and the slope

Case 4 : Slope and the x-intercept

Case #1Case #1 – Given – Given two coordinatestwo coordinates

Example(4,3) , (7,9)Find the slope1. M = (9-3) / (7-4) = (6/3) = 22. Y = 2x + b 3. Choose 1 point to substitute 4. Y = 2x=b 3 = 2(4) + b b = -55. Y = 2x-5

Case #2Case #2 – Given – Given slope and y -interceptslope and y -intercept

Example

1. m = -2, y-int = or b=6

2. y = mx+b

3. y = -2x +6

Case #3Case #3 – Given – Given one coordinate and the slopeone coordinate and the slope

Example

(x,y) = (3,-1) , m=2

1. Y = 2x+b

2. –1= 6+b

3. –7=b

4. Y = 2x-7

Case #4Case #4 – Given – Givenslope and the x -interceptslope and the x -intercept

Example

m = 5 , x-int = 3 (3,0)

1. Y = 5x+b

2. 0 = 5(3)+b

3. –15 = b

4. Y= 5x-15

4.54.5 - Interpreting the Equation - Interpreting the Equation Ax + By + C = 0Ax + By + C = 0

Determining the slope, x- intercept, and y-intercept

Ax + By + C = 0

By = -Ax –C

Y = -(-A/B) + (-C/B) Slope = (-A/B) Y intercept = (-C/B) Ax = -C X = (-C/A) X intercept = (-C/A)

4.54.5 - Interpreting the Equation - Interpreting the Equation Ax + By + C = 0Ax + By + C = 0

Example

Find slope, y-int, and x-int for this equation. Graph the equation

2x + 4y + 8 = 0

1. Slope : (-A/B) = (-2/4) = (-1/2)

2. Y-int : (-C/B) = (-8/4) = (-2)

3. X-int : (-C/A) = (-8/2) = (-4)

4. Equation : y = (-1/2)x -2

5. Graph : - - - - - - - - - - - - - - - -