Cracking the Code: Equations of Lines with Perpendicularity

Algebra 2 Grades High School 8:27 Video
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Lesson Description

Learn how to determine the equation of a line in slope-intercept form given a point and a perpendicular line. This lesson builds upon the concept of perpendicular slopes and applies algebraic manipulation to find the equation of the desired line.

Video Resource

Equation of Line Slope intercept Form | Given Point and Perpendicular Line

Kevinmathscience

Duration: 8:27
Watch on YouTube

Key Concepts

  • Slope-intercept form (y = mx + b)
  • Perpendicular lines and their slopes (m1 * m2 = -1)
  • Substituting a point into an equation to solve for an unknown (y = mx + b)

Learning Objectives

  • Students will be able to determine the slope of a line perpendicular to a given line.
  • Students will be able to write the equation of a line in slope-intercept form given a point on the line and the equation of a perpendicular line.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the slope-intercept form of a linear equation (y = mx + b). Discuss the relationship between slopes of parallel lines (equal slopes) and introduce the concept of perpendicular lines intersecting at a 90-degree angle. Briefly explain that the product of the slopes of perpendicular lines is -1.
  • Video Viewing (10 mins)
    Play the Kevinmathscience video 'Equation of Line Slope intercept Form | Given Point and Perpendicular Line'. Encourage students to take notes on the key steps and formulas presented in the video.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video. Start with simpler examples and gradually increase the complexity. Emphasize the steps: 1. Find the slope of the given perpendicular line. 2. Calculate the slope of the line we want to find (using m1 * m2 = -1). 3. Use the given point and the calculated slope to find the y-intercept (b) in y = mx + b. 4. Write the equation of the line in slope-intercept form.
  • Independent Practice (10 mins)
    Provide students with practice problems to solve independently. Circulate to offer assistance and answer questions.
  • Wrap-up (5 mins)
    Review the key concepts and steps. Answer any remaining questions. Preview the upcoming topic.

Interactive Exercises

  • Slope Challenge
    Present students with equations of lines. They must quickly determine the slope of a line perpendicular to each given line. Increase the pace to challenge their understanding.
  • Equation Builder
    Provide pairs of students with a point and the equation of a perpendicular line. They must work together to find the equation of the line passing through the point and perpendicular to the given line. The first pair to correctly solve the problem earns a bonus.

Discussion Questions

  • What is the relationship between the slopes of perpendicular lines?
  • Why is it important to rewrite the equation of a line in slope-intercept form before determining its slope?
  • How does knowing a point on a line help us find its equation?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking
  • Analytical Skills

Multiple Choice Questions

Question 1:

What is the slope of a line perpendicular to a line with a slope of 2/3?

Correct Answer: -3/2

Question 2:

The equation of a line is y = -4x + 5. What is the slope of a line perpendicular to this line?

Correct Answer: 1/4

Question 3:

A line has a slope of -1. What is the slope of a line perpendicular to it?

Correct Answer: 1

Question 4:

What is the y-intercept in the slope-intercept equation y = mx + b?

Correct Answer: b

Question 5:

If two lines are perpendicular, the product of their slopes is always equal to:

Correct Answer: -1

Question 6:

A line is perpendicular to y = (1/5)x + 2. If the perpendicular line passes through (0, 0), what is its equation?

Correct Answer: y = -5x

Question 7:

Line 1 has slope m1 and Line 2 has slope m2. Which equation is correct if the lines are perpendicular?

Correct Answer: m1 * m2 = -1

Question 8:

To determine the slope of a line from an equation not in slope-intercept form, you must first:

Correct Answer: Solve for y

Question 9:

The slope-intercept form of a line equation is:

Correct Answer: y = mx + b

Question 10:

Which of the following steps is NOT needed when finding the equation of a perpendicular line in slope-intercept form?

Correct Answer: Determine the midpoint of the line

Fill in the Blank Questions

Question 1:

The slope-intercept form of a linear equation is y = mx + ____.

Correct Answer: b

Question 2:

If two lines are perpendicular, the product of their slopes equals ____.

Correct Answer: -1

Question 3:

The lines intersect each other at a 90° angle.

Correct Answer: perpendicular

Question 4:

To find the slope of a line perpendicular to y = 5x + 3, you first determine the slope of the given line which is ____.

Correct Answer: 5

Question 5:

If a line has a slope of 4, a perpendicular line would have a slope of ____.

Correct Answer: -1/4

Question 6:

The y-intercept is the point where the line crosses the ____-axis.

Correct Answer: y

Question 7:

If a line is horizontal, the slope of a line perpendicular to it is ____.

Correct Answer: undefined

Question 8:

To write the equation of the line, after finding the slope of the perpendicular line, you must calculate the ____.

Correct Answer: y-intercept

Question 9:

In the equation y = mx + b, m represents the ____ of the line.

Correct Answer: slope

Question 10:

If a line is in the form Ax + By = C, it must be converted to ____-____ form before finding its slope.

Correct Answer: slope-intercept

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies. A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together).

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