Holt Geometry 3-6 Lines in the Coordinate Plane 3-6 Lines in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

Holt Geometry 3-6 Lines in the Coordinate Plane Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 Solve each equation for y. 3. y – 6x = 9 2. m = –1, x = 5, and y = –4 b = –6 b = x – 2y = 8 y = 6x + 9 y = 2x – 4

Holt Geometry 3-6 Lines in the Coordinate Plane Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. Objectives

Holt Geometry 3-6 Lines in the Coordinate Plane point-slope form slope-intercept form Vocabulary

Holt Geometry 3-6 Lines in the Coordinate Plane

Holt Geometry 3-6 Lines in the Coordinate Plane Find the slope and y-intercept of each line and then graph each line.

Holt Geometry 3-6 Lines in the Coordinate Plane y = 2x + 5

Holt Geometry 3-6 Lines in the Coordinate Plane y = - x – 7 1 2

Holt Geometry 3-6 Lines in the Coordinate Plane y = 3x

Holt Geometry 3-6 Lines in the Coordinate Plane y = 3

Holt Geometry 3-6 Lines in the Coordinate Plane y = - 4x + 3

Holt Geometry 3-6 Lines in the Coordinate Plane x = 4

Holt Geometry 3-6 Lines in the Coordinate Plane x – 2y = 6

Holt Geometry 3-6 Lines in the Coordinate Plane 4x + 3y = -3

Holt Geometry 3-6 Lines in the Coordinate Plane x – y = 2

Holt Geometry 3-6 Lines in the Coordinate Plane 5x + 3y = 0

Holt Geometry 3-6 Lines in the Coordinate Plane x = 6

Holt Geometry 3-6 Lines in the Coordinate Plane - x + 5y + 5 = 0

Holt Geometry 3-6 Lines in the Coordinate Plane 0 = -2x – y - 3

Holt Geometry 3-6 Lines in the Coordinate Plane -3x = -5 – y

Holt Geometry 3-6 Lines in the Coordinate Plane Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 5 and a y-intercept of -2

Holt Geometry 3-6 Lines in the Coordinate Plane Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 0 and a y-intercept of 3

Holt Geometry 3-6 Lines in the Coordinate Plane Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 6 through (3, –4)

Holt Geometry 3-6 Lines in the Coordinate Plane Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope -2 through (-2, 4)

Holt Geometry 3-6 Lines in the Coordinate Plane Example 1B: Writing Equations In Lines Write the equation of each line in the given form. the line through (–1, 0) and (1, 2)

Holt Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 1a Write the equation of each line in the given form. the line with slope 0 through (4, 6)

Holt Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 1b Write the equation of each line in the given form. the line through (–3, 2) and (1, 2)

Holt Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 1b Write the equation of each line in the given form. the line through (–7, 9) and (-4, -2)

Holt Geometry 3-6 Lines in the Coordinate Plane A system of two linear equations in two variables represents two lines. The lines can be parallel, intersecting, or coinciding. Lines that coincide are the same line, but the equations may be written in different forms.

Holt Geometry 3-6 Lines in the Coordinate Plane

Holt Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3A: Classifying Pairs of Lines y = 3x + 7, y = –3x – 4

Holt Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3B: Classifying Pairs of Lines

Holt Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3C: Classifying Pairs of Lines 2y – 4x = 16, y – 10 = 2(x - 1)

Holt Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 3 3x + 5y = 2 and 3x + 6 = -5y

Holt Geometry 3-6 Lines in the Coordinate Plane Lesson Quiz: Part I Write the equation of each line in the given form. Then graph each line. 1. the line through (-1, 3) and (3, -5) in slope- intercept form. y = –2x y + 1 = (x – 5) 2. the line through (5, –1) with slope in point-slope form.

Holt Geometry 3-6 Lines in the Coordinate Plane Lesson Quiz: Part II Determine whether the lines are parallel, intersect, or coincide. 3. y – 3 = – x, intersect 1 2 y – 5 = 2(x + 3) 4. 2y = 4x + 12, 4x – 2y = 8 parallel