Presentation on theme: "GOAL 1 SLOPE OF PARALLEL LINES EXAMPLE 1 3.6 PARALLEL LINES IN THE COORDINATE PLANE y2 - y1y2 - y1 m = x2 - x1x2 - x1."— Presentation transcript:
GOAL 1 SLOPE OF PARALLEL LINES EXAMPLE PARALLEL LINES IN THE COORDINATE PLANE y2 - y1y2 - y1 m = x2 - x1x2 - x1
Extra Example 1 The Cog Railway covers about 3.1 miles and gains about 3600 feet of altitude. What is the average slope of the track?
m = run change in x rise change in y = = y2 - y1y2 - y1 x2 - x1x2 - x1 y2 - y1y2 - y1 m = x2 - x1x2 - x1 The order of subtraction is important. You can label either point as (x 1, y 1 ) and the other point as (x 2, y 2 ). However, both the numerator and denominator must use the same order. numerator y2 - y1y2 - y1 denominator x2 - x1x2 - x1 When you use the formula for the slope, Subtraction order is the same the numerator and denominator must use the same subtraction order. CORRECT x1 - x2x1 - x2 y2 - y1y2 - y1 Subtraction order is different INCORRECT EXAMPLE 2
Extra Example 2 Find the slope of a line that passes through the points (–3, 0) and (4, 7).
EXAMPLE 3 POSTULATE In the coordinate plane, nonvertical lines are parallel if and only if they have the same slope. Vertical lines are parallel.
Extra Example 3 Find the slope of each line. EXAMPLE 4
Extra Example 4 Line p 1 passes through (0, –3) and (1, –2). Line p 2 passes through (5, 4) and (–4, –4). Line p 3 passes through (–6, –1) and (3, 7). Find the slope of each line. Which lines are parallel?
Checkpoint Line k 1 passes through (8, –1) and (–5, –9). Line k 2 passes through (–6, –5) and (7, 3). Line k 3 passes through (10, –4) and (–3, –4). Find the slope of each line. Which lines are parallel?
GOAL 2 WRITING EQUATIONS OF PARALLEL LINES EXAMPLE PARALLEL LINES IN THE COORDINATE PLANE We will write equations in slope-intercept form:
Extra Example 5 Write an equation of the line through the point (4, 9) that has a slope of –2.
Checkpoint Write an equation of the line through the point (20, 5) that has a slope of EXAMPLE 6
Extra Example 6 Line k 1 has the equation Line k 2 is parallel to k 1 and passes through the point (–5, 0). Write an equation of k 2.
Checkpoint Line m 1 has the equation y = 3x – 7. Line m 2 is parallel to m 1 and passes through the point (–2, 1). Write an equation of m 2.
QUESTION: ANSWER: What are the six methods we have available to prove two lines are parallel? 1-3: Show alternate interior angles, alternate exterior angles, or corresponding angles are congruent. 4: Show consecutive interior angles are supplementary. 5: Show that the lines are perpendicular to the same line. 6: Show that the lines are parallel to the same line.