3.5 Lines in the Coordinate Plane

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Presentation transcript:

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

Graphing Lines in Slope-Intercept Form Graph the line y = -½x – 2 m = b = Graph the line y = ½x – 1 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)

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: (2, 6) Horizontal:

Homework pg 155 1-37all Workbook 3.5 All Show all work on a separate sheet of paper