Perpendicular Lines: From Point-Slope to Standard Form

Algebra 2 Grades High School 4:13 Video
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Lesson Description

Learn how to derive the equation of a line in standard form when given a point and a perpendicular line. This lesson reinforces the relationship between slopes of perpendicular lines and algebraic manipulation.

Video Resource

Equation of Line Standard Form | Given Point and Perpendicular Line

Kevinmathscience

Duration: 4:13
Watch on YouTube

Key Concepts

  • Slope-intercept form (y = mx + b)
  • Standard form (Ax + By = C)
  • Perpendicular lines and their slopes (m1 * m2 = -1)
  • Algebraic manipulation to convert between forms

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 and the slope.
  • Students will be able to convert a linear equation from slope-intercept form to standard form.
  • Students will be able to identify the conditions for an equation to be in standard form (A, B, and C are integers, and A is positive).

Educator Instructions

  • Introduction (5 mins)
    Briefly review the concepts of slope, slope-intercept form, and standard form. Remind students of the relationship between slopes of perpendicular lines (m1 * m2 = -1). Preview the video and its learning objectives.
  • Video Viewing (10 mins)
    Play the video 'Equation of Line Standard Form | Given Point and Perpendicular Line' by Kevinmathscience. Encourage students to take notes on the key steps.
  • Guided Practice (15 mins)
    Work through an example problem similar to the one in the video, step-by-step. Emphasize each step: finding the perpendicular slope, using the point-slope form (optional, but can be mentioned), converting to slope-intercept form, and finally, converting to standard form. Address student questions and misconceptions.
  • Independent Practice (15 mins)
    Provide students with practice problems to solve independently. Offer assistance as needed. The problems should involve finding the equation of a line in standard form, given a point and a perpendicular line.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and steps. Administer a short quiz (multiple choice or fill-in-the-blank) to assess student understanding.

Interactive Exercises

  • Online Equation Converter
    Use an online tool (e.g., Desmos, Wolfram Alpha) to convert equations between slope-intercept and standard form. Students can check their answers and explore different equations.
  • Group Challenge
    Divide students into groups and give each group a different point and a perpendicular line's equation. Have them race to find the equation of the line in standard form. The first group to correctly solve the problem wins.

Discussion Questions

  • Why is it important for 'A' to be positive in the standard form equation?
  • Can you think of a situation in real life where perpendicular lines and standard form equations might be useful?
  • What are the advantages and disadvantages of using slope-intercept form versus standard form?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Analytical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the slope of a line perpendicular to y = 2x + 3?

Correct Answer: -1/2

Question 2:

Which of the following equations is in standard form?

Correct Answer: 2x + y = 7

Question 3:

What must be true about A in the standard form equation Ax + By = C?

Correct Answer: It must be positive

Question 4:

If a line has a slope of -3, the slope of a line perpendicular to it is:

Correct Answer: 1/3

Question 5:

Which form is the equation y = mx + b?

Correct Answer: Slope-Intercept Form

Question 6:

The equation of a line perpendicular to y = -1/4x + 2 that passes through the point (0,0) is...

Correct Answer: y = 4x

Question 7:

Given the point (2,3) and a perpendicular slope of -1, what is the y-intercept of the line?

Correct Answer: 5

Question 8:

In the standard form equation 5x + 2y = 8, what is the value of B?

Correct Answer: 2

Question 9:

What is the first step in converting slope intercept form to standard form?

Correct Answer: Rearrange the equation to move the x term to the left side

Question 10:

If a line is vertical, what is the slope of any line perpendicular to it?

Correct Answer: 0

Fill in the Blank Questions

Question 1:

The product of the slopes of two perpendicular lines is always ______.

Correct Answer: -1

Question 2:

The standard form of a linear equation is written as Ax + By = ____.

Correct Answer: C

Question 3:

To convert from slope-intercept form to standard form, move the _____ term to the left side of the equation.

Correct Answer: x

Question 4:

If a line has a slope of 5, a line perpendicular to it has a slope of ______.

Correct Answer: -1/5

Question 5:

In standard form, 'A' must be a _______ number.

Correct Answer: positive

Question 6:

The equation y = mx + b is in _________ form.

Correct Answer: slope-intercept

Question 7:

If two lines are parallel, their slopes are __________.

Correct Answer: equal

Question 8:

Given the point (1,4) and a perpendicular slope of 2, the y-intercept is ______.

Correct Answer: 2

Question 9:

When finding the equation of a perpendicular line, the first step is to determine the ___________ slope.

Correct Answer: perpendicular

Question 10:

In the equation 3x + 4y = 12, the x and y intercepts are ________ and _________ respectively.

Correct Answer: 4, 3

Educational Standards

A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies. 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.

Teaching Materials

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