Presentation on theme: "3.6 PARALLEL LINES IN THE COORDINATE PLANE 1 m = GOAL"— Presentation transcript:
1 3.6 PARALLEL LINES IN THE COORDINATE PLANE 1 m = GOAL SLOPE OF PARALLEL LINESy2 - y1m =x2 - x1EXAMPLE 1
2 Extra Example 1The Cog Railway covers about 3.1 miles and gains about 3600 feet of altitude. What is the average slope of the track?
3 m = m = = When you use the formula for the slope, y2 - y1m =x2 - x1m =run change in xrise change in y=y2 - y1x2 - x1Subtraction order is the samethe numerator and denominatormust use the same subtraction order.CORRECTx1 - x2y2 - y1Subtraction order is differentINCORRECTThe order of subtraction is important. You can label either point as (x1, y1)and the other point as (x2, y2). However, both the numerator and denominatormust use the same order.numeratory2 - y1denominatorx2 - x1EXAMPLE 2
4 Extra Example 2Find the slope of a line that passes through the points(–3, 0) and (4, 7).
5 Vertical lines are parallel. POSTULATEIn the coordinate plane, nonvertical lines are parallel if and only if they have the same slope.Vertical lines are parallel.EXAMPLE 3
6 Extra Example 3Find the slope of each line.EXAMPLE 4
7 Extra Example 4Line p1 passes through (0, –3) and (1, –2). Line p2 passes through (5, 4) and (–4, –4). Line p3 passes through (–6, –1) and (3, 7). Find the slope of each line. Which lines are parallel?
8 CheckpointLine k1 passes through (8, –1) and (–5, –9). Line k2 passes through (–6, –5) and (7, 3). Line k3 passes through (10, –4) and (–3, –4). Find the slope of each line. Which lines are parallel?
9 We will write equations in slope-intercept form: 3.6PARALLEL LINES IN THE COORDINATE PLANEGOAL2WRITING EQUATIONS OF PARALLEL LINESWe will write equations in slope-intercept form:EXAMPLE 5
10 Extra Example 5Write an equation of the line through the point (4, 9) that has a slope of –2.
11 CheckpointWrite an equation of the line through the point (20, 5) that has a slope ofEXAMPLE 6
12 Extra Example 6 Line k1 has the equation Line k2 is parallel to k1 and passes through the point (–5, 0). Write an equationof k2.
13 CheckpointLine m1 has the equation y = 3x – 7. Line m2 is parallel to m1 and passes through the point (–2, 1). Write an equation of m2.
14 QUESTION:What are the six methods we have available to prove two lines are parallel?ANSWER: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.