Lesson 5: 4-3 Parallel & Perpendicular Lines (alternative method)
Duration of Days: 4
Lesson Objective
Write an equation of the line that passes through a given point, parallel to a given line.
Write an equation of the line that passes through a given point, perpendicular to a given line.
If a given line is vertical, what is the slope of any line parallel to the given line? perpendicular to the given line?
What is the relationship between the slopes of two perpendicular lines? What is the product of the slopes?
paralell lines
perpendicular lines
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
SAT questions related to writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19
functions: 8-4-4, 7-4-18, 8-4-18, 2-4-14, 3-4-20, 1-4-5, 7-4-21,
Solving Equations: 5-3-17, 6-4-32, 3-4-7, 8-3-1, 3-3-17, 6-3-17, 1-3-1, 3-3-2, 2-3-1, 7-3-16, 6-3-6,
When two distinct lines lie in the same plane and have the same slope, they are parallel. When two lines do not have the same slope, they intersect. If two oblique lines intersect at right angles, forming perpendicular lines, the slopes of the two lines are negative reciprocals of each other, and the product of their slopes is –1.
has endpointsOn the plans for a treehouse, a beam represented by line QR has endpoints Q(-6,2) and R(-1,8). A connecting beam represented by line ST has endpoints S(-3,6) and T(-8, 5). Are the beams perpendicular? Explain.
Encourage students to understand the process used instead of simply the mechanics. For example, what do they know from the given information? What do they know about perpendicular lines? What do they need to know to write a new equation?
Students may be familiar with the terms parallel and perpendicular. However, before covering the examples, you may want students to use rulers to draw parallel and perpendicular lines on graph paper.
Extension: Write A(-4, -1), B(1, 4), C(4, 1), and D(-1, -4) on the board. Ask students to determine what geometric figure is made if they were to connect these points to get a polygon. Ask students to justify their answer.
Practice Exercises 1-10
Exercises 49-54
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