Lines in the Coordinate Plane Objectives: Graphing lines in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding.

a. Write the equation of the line with slope 3 through (2,1) in point-slope form. b. Write the equation of the line through (0,4) and (-1,2) in slope-intercept form.

Example 1: Graphing Lines Graph each line. The equation is given in the slope-intercept form, with a slope of and a y-intercept of 1. Plot the point (0, 1) and then rise 1 and run 2 to find another point. Draw the line containing the points. (0, 1) rise 1 run 2

Example 2: Graphing Lines Graph each line. y – 3 = –2(x + 4) The equation is given in the point-slope form, with a slope of through the point (–4, 3). Plot the point (–4, 3) and then rise –2 and run 1 to find another point. Draw the line containing the points. (–4, 3) rise –2 run 1

Example 3: Graphing Lines Graph each line. y = –3 The equation is given in the form of a horizontal line with a y-intercept of –3. The equation tells you that the y-coordinate of every point on the line is –3. Draw the horizontal line through (0, –3). (0, –3)

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.

If coplanar lines are not parallel or the same line, then they will eventually intersect.

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

Example B: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. Solve the second equation for y to find the slope-intercept form. 6y = –2x + 12 Both lines have a slope of , and the y-intercepts are different. So the lines are parallel.

Example C: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. 2y – 4x = 16, y – 10 = 2(x - 1) Solve both equations for y to find the slope-intercept form. 2y – 4x = 16 y – 10 = 2(x – 1) 2y = 4x + 16 y – 10 = 2x - 2 y = 2x + 8 y = 2x + 8 Both lines have a slope of 2 and a y-intercept of 8, so they coincide.

Check It Out! Determine whether the lines 3x + 5y = 2 and 3x + 6 = -5y are parallel, intersect, or coincide. Solve both equations for y to find the slope-intercept form. 3x + 5y = 2 3x + 6 = –5y 5y = –3x + 2 Both lines have the same slopes but different y-intercepts, so the lines are parallel.

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

a. Graph y = 3/2 x + 3 b. Graph y + 3 = -2 (x-1) c. Graph x = 3 d. Graph y = 2x – 3 e. Graph y – 1 = -2/3 (x + 2) f. Graph y = -4

Determine whether the lines are parallel, intersect, or coincide. y = 2x + 3 and y = 2x – 1 y = 3x – 5 and 6x – 2y = 10 3x + 2y = 7 and 3y = 4x + 7

d. 3x + 5y = 2 and 3x + 6 = -5y e. 4x + 2y = 10 and y = -2x + 15 f. 7x + 2y = 10 and 3y = 4x – 5 g. 6x – 12 y = - 24 and 3y = 2x + 18