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Algebra 1 5-4 Complete Lesson: Point-Slope Form

By Matt Richardson
Last updated almost 3 years ago
24 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! The red line shows the altitude of a hot-air balloon during its linear descent. What is an equation of the line in slope-intercept form? Hint: What is the altitude of the balloon when it starts its descent at x = 0?

Problem 1 Got It?

Problem 2 Got It? What is the graph of the equation?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It? In the last step of Problem 3, use the point (-2, -3) instead of (1, 4) to write an equation of the line.

Problem 3 Got It? Reasoning: Rewrite the equations in Problem 3 and in the previous item in slope-intercept form. Compare the two rewritten equations. What can you conclude?

Problem 4 Got It? The table shows the number of gallons of water y in a tank after x hours. The relationship is linear. What is an equation in point-slope form that models the data? What does the slope represent?

Problem 4 Got It? Reasoning: Rewrite the equation from the previous item in slope-intercept form. What does the y-intercept represent?

What are the slope and one point on the graph of the equation below?

What is an equation of the line that passes through the point (3, -8) and has slope -2?

What is an equation of the line that passes through the points (-1, -2) and (2, 4)?

What is the graph of the equation below?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Vocabulary: What features of the graph of the equation below can you identify?

Reasoning: Does the graph of the equation below include the point (-2, 1)? Explain.

Reasoning: Can any equation in point-slope form also be written in slope-intercept form? Give an example to explain.

Review Lesson 5-3: Match the slopes m and y-intercepts b with their equations.

  • m = 1
  • m = -1
  • m = 6
  • b = 0
  • b = 4
  • b = -13
  • y = x + 4
  • y = 6x
  • y = -x - 13

Review Lesson 2-5: Solve the equation for y.

Review Lesson 2-5: Solve the equation for y.

Review Lesson 2-5: Solve the equation for y.

Vocabulary Review: Classify each equation based on its y-intercept.

  • y = 3x + 4
  • y = 4x - 3
  • y = 5x + 3
  • y = -3x + 2
  • Has a y-intercept of 3
  • Has a y-intercept other than 3

Vocabulary Review: Categorize each equation based on whether or not it is in slope-intercept form.

  • 2x - y = 10
  • x + 3y + 11 = 0
  • y - 4 = 2(x + 7)
  • y = 2x + 6
  • Slope-intercept form
  • NOT Slope-intercept form

Vocabulary Review: Classify each statement based on whether or not it is true about the y-intercept of any graph.

  • occurs where y = 0 on the graph
  • occurs where x = 0 on the graph
  • occurs where the graph touches the x-axis
  • True of the y-intercept of any graph
  • NOT true of the y-intercept (of at least some graphs)

Use Your Vocabulary: Complete each sentence with the appropriate word from the list.

  • price
  • sun
  • time
  • The length of a shadow is a function of the angle of the __?__.
  • The amount of water that has leaked from a leaky faucet is a function of __?__.
  • The amount of sales tax you pay is a function of the item's __?__.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success