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

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 b = –6 2. m = –1, x = 5, and y = –4 b = 1 y = 6x + 9 4. 4x – 2y = 8 y = 2x – 4

Objectives Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding.

Vocabulary point-slope form slope-intercept form

A line with y-intercept b contains the point (0, b). A line with x-intercept a contains the point (a, 0). Remember!

Example 1A: Writing Equations In Lines Write the equation of each line in the given form. the line with slope 6 through (3, –4) in point-slope form

Example 1C: Writing Equations In Lines Write the equation of each line in the given form. the line with the x-intercept 3 and y-intercept –5 in point slope form

Check It Out! Example 1a Write the equation of each line in the given form. the line with slope 0 through (4, 6) in slope-intercept form

Check It Out! Example 1b Write the equation of each line in the given form. the line through (–3, 2) and (1, 2) in point-slope form

Example 2A: Graphing Lines Graph each line. (0, 1) rise 1 run 2

Example 2B: Graphing Lines Graph each line. y – 3 = –2(x + 4) (–4, 3) rise –2 run 1

Example 2C: Graphing Lines Graph each line. y = –3 (0, –3)

Check It Out! Example 2a Graph each line. y = 2x – 3 run 1 rise 2 (0, –3) rise 2 run 1

Check It Out! Example 2b Graph each line. The equation is given in the point-slope form, with a slope of through the point (–2, 1). Plot the point (–2, 1)and then rise –2 and run 3 to find another point. Draw the line containing the points. (–2, 1) run 3 rise –2

Check It Out! Example 2c Graph each line. y = –4 The equation is given in the form of a horizontal line with a y-intercept of –4. The equation tells you that the y-coordinate of every point on the line is –4. Draw the horizontal line through (0, –4). (0, –4)

A system of two linear equations in two variables represents two lines 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.

Example 3A: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. y = 3x + 7, y = –3x – 4

Example 3B: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide.

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

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 + 1 2. the line through (5, –1) with slope in point-slope form. 2 5 y + 1 = (x – 5)

Lesson Quiz: Part II Determine whether the lines are parallel, intersect, or coincide. 1 2 3. y – 3 = – x, y – 5 = 2(x + 3) intersect 4. 2y = 4x + 12, 4x – 2y = 8 parallel