3.5 Lines in the Coordinate Plane Chapter 3: Parallel and Perpendicular Lines.

3.5 Lines in the Coordinate Plane

Chapter 3: Parallel and Perpendicular Lines

3.5 Lines in the Coordinate Plane

Slope-Intercept Form: y = mx + b

m: slope

b: y-intercept

(x, y): point

Slope-Intercept Form

Identify the slope and y-intercept for each:

a. y = 3x + 2 b. y = -2x + 5

c. y = ½x – 5 d. y = 3x – ½

e. y = -5x – 4 f. y = 0.2x + 0.7

Graphing Lines in Slope-Intercept Form Graph the line y = 3/4x + 2

m = b =

Graph the line y = x + 2

m = b =

Graph the line y = 3x + 4

m = b =

Graphing Lines in Slope-Intercept Form Graph the line y = -½x – 2

m = b =

Graph the line y = ½x – 1

m = b =

Graph the line y = -5/3 x + 2

m = b =

Standard Form

Ax + By = C

(3x + 2y = 5)

To Graph from Standard Form, find the x- and y- intercepts:

To find the x-intercept, plug in 0 for y.

To find the y-intercept, plug in 0 for x.

Graphing Using Intercepts

Graph 6x + 3y = 12

Find the x-intercept:

Find the y-intercept:

Graphing Using Intercepts

Graph -2x + 4y = -8

Find the x-intercept:

Find the y-intercept:

Transforming to Slope-Intercept Form

Graph 4x – 2y = 9, using slope-intercept form:

Transforming to Slope-Intercept Form

Graph -5x + y = -3, using slope-intercept form:

Write each equation in slope-intercept form and graph the line: y = 2x + 1 y – 1 = x y + 2x =4 8x + 4y = 16 2x + 6y = 6 ¾x – ½y = 1/8

Point-Slope Form

y – y1 = m(x – x1)

(1, 3) and slope 2: (y – 3) = 2(x – 1)

y – y1 = m(x – x1)

Using Point-Slope Form

Write an equation of the line through point

P(-1, 4) with slope 3.

y – y1 = m(x – x1)

y – y1 = m(x – x1)

Using Point-Slope Form

Write an equation of the line through point

P(2, -4) with slope -1.

Write an equation of the line in point-slope form: P(2, 3), slope = 2 I(4, -1), slope = 3 R(-2, -6), slope = -4 A(6, 1), slope = ½ T(-3, 5), slope -1 E(0, 4), slope 1

Writing an Equation of a Line Given Two Points: Write an equation of the line through A(-2,3) and

B(1,-1):

Find the slope:

Use one point and write the equation in point-slope form:

Writing an Equation of a Line Given Two Points: Write an equation of the line through P(5,0) and

Q(7,-3)

Find the slope:

Use one point and write the equation in point-slope form:

Write an equation in point-slope form of the line that contains the given points: D(0,5) E(5,8)

F(6,2) G(2,4)

H(2,6) I(-1,3)

J(-4,4) K(2,10)

L(-1,0) M(-3,-1)

N(8,10) O(-4,2)

Equations of Horizontal and Vertical Lines: A Horizontal Line cuts through the y-axis, so

the equation is y = A Vertical Line cuts through the x-axis, so the

equation is x =

y = 4 x = 3

Equations of Horizontal and Vertical Lines: Write the Equations of the Horizontal and

Vertical line that goes through the point: (3, 2) Horizontal:

Vertical: (4, 7) Horizontal:

Vertical: (2, 6) Horizontal:

Vertical:

Homework

pg 155 1-37all Workbook 3.5 All

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