3 6 Linesininthe the Coordinate Plane Warm Up

3 -6 Linesininthe the. Coordinate. Plane Warm Up Lesson Presentation 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 b = – 6 2. m = – 1, x = 5, and y = – 4 b = 1 Solve each equation for y. 3. y – 6 x = 9 y = 6 x + 9 4. 4 x – 2 y = 8 y = 2 x – 4 Holt Geometry

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

3 -6 Lines in the Coordinate Plane Vocabulary point-slope form slope-intercept form 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 = 2 x + 5 Holt Geometry

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

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

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

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

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

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

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

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

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

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

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

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

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

3 -6 Lines in the Coordinate Plane Example 1 A: 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 1 A: 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 1 A: 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 1 A: 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 1 B: 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 1 a 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 1 b 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 1 b 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 Example 3 A: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. y = 3 x + 7, y = – 3 x – 4 Holt Geometry

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

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

3 -6 Lines in the Coordinate Plane Check It Out! Example 3 3 x + 5 y = 2 and 3 x + 6 = -5 y 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 slopeintercept form. y = – 2 x + 1 2. the line through (5, – 1) with slope in point-slope form. y + 1 = 2 (x – 5) 5 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 = – 1 x, y – 5 = 2(x + 3) 2 intersect 4. 2 y = 4 x + 12, 4 x – 2 y = 8 parallel Holt Geometry